BACKGROUND Spinal cord injury(SCI)often results in irreversible neurological deficits;therefore,effective treatment is urgently needed.Neural stem cells(NSCs)have excellent differentiation potential.However,the role o...BACKGROUND Spinal cord injury(SCI)often results in irreversible neurological deficits;therefore,effective treatment is urgently needed.Neural stem cells(NSCs)have excellent differentiation potential.However,the role of the long noncoding RNA X inactive-specific transcript(XIST)in NSCs and SCI remains unclear.AIM To explore the role of XIST in enhancing NSC function and its therapeutic potential in SCI.METHODS We used in vitro and in vivo models to examine the effects of XIST on NSCs.XIST was overexpressed in NSCs,and its impact on mitochondrial function,neuronal differentiation,and the insulin-like growth factor 2 mRNA binding protein 2(IGF2BP2)/carnitine palmitoyl transferase 1A(CPT1A)pathway was assessed using a series of biochemical assays,quantitative PCR,and Seahorse XF24 analysis.A mouse model of SCI was used to evaluate the therapeutic effects of XIST in vivo.RESULTS Overexpression of XIST in NSCs significantly increased mitochondrial membrane potential,ATP production,and oxygen consumption rate.XIST also promoted NSC proliferation and neuronal differentiation while inhibiting astrocytic differentiation.Mechanistically,XIST regulated CPT1A expression post-transcriptionally by interacting with IGF2BP2.In vivo XIST-treated mice exhibited improved motor scores and reduced proinflammatory cytokine expression following SCI.CONCLUSIONThese findings suggested that XIST modulated mitochondrial function and neural differentiation in NSCs throughthe IGF2BP2/CPT1A pathway. While preliminary in vivo results are encouraging, further studies are needed todetermine the long-term therapeutic relevance and underlying mechanisms of XIST in SCI recovery.展开更多
This study focuses on the three courtyards located in the eastern,central,and western sections of the Tongzhou Campus of Renmin University of China.Adopting a functional differentiation perspective,the research system...This study focuses on the three courtyards located in the eastern,central,and western sections of the Tongzhou Campus of Renmin University of China.Adopting a functional differentiation perspective,the research systematically analyzes the patterns of plant diversity within courtyards characterized by distinct functional orientations.This analysis employs various plant species diversity indices,including the Patrick richness index,Simpson dominance index,Shannon-Wiener diversity index,and Pielou evenness index,alongside a classification of functional plant types,namely ornamental,ecological regulation,spatial shaping,and recreational assistance.The results indicate that the east courtyard presents the highest Patrick species richness(S=42),predominantly comprising spatial shaping and recreational assistance plants,which are wellsuited for recreational and passage functions.Conversely,the central courtyard exhibits the lowest Patrick species richness(S=19),characterized by a balanced distribution of functional types,with an emphasis on public display and traffic guidance.The west courtyard demonstrates the greatest stability in the tree layer(D=0.87),featuring a combination of shade-tolerant and ornamental plants that fulfill the requirements for a tranquil and naturalistic environment.One-way analysis of variance reveals that only Patrick species richness differs significantly among the courtyards(P=0.007),whereas the diversity index does not show a significant difference.This finding suggests that functional requirements precisely regulate diversity through microhabitat heterogeneity and plant configuration strategies.This study offers both a theoretical foundation and practical guidance for the plant configuration and functional optimization of small-scale courtyards on campus.展开更多
This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node...This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.展开更多
The purpose of this paper is to add some complements to the general theory of higher-order types of asymptotic variation developed in two previous papers so as to complete our elementary (but not too much!) theory in ...The purpose of this paper is to add some complements to the general theory of higher-order types of asymptotic variation developed in two previous papers so as to complete our elementary (but not too much!) theory in view of applications to the theory of finite asymptotic expansions in the real domain, the asymptotic study of ordinary differential equations and the like. The main results concern: 1) a detailed study of the types of asymptotic variation of an infinite series so extending the results known for the sole power series;2) the type of asymptotic variation of a Wronskian completing the many already-published results on the asymptotic behaviors of Wronskians;3) a comparison between the two main standard approaches to the concept of “type of asymptotic variation”: via an asymptotic differential equation or an asymptotic functional equation;4) a discussion about the simple concept of logarithmic variation making explicit and completing the results which, in the literature, are hidden in a quite-complicated general theory.展开更多
This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of...This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).展开更多
A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined e...A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.展开更多
Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defin...Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.展开更多
This paper investigates the optimal Lagrange interpolation of a class F∞of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,ω)[-1,1],1≤p<∞withωa continuous integrable weight ...This paper investigates the optimal Lagrange interpolation of a class F∞of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,ω)[-1,1],1≤p<∞withωa continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation polynomials based on the zeros of polynomials with the leading coefficient 1 of the least deviation from zero in L_(p,ω)[-1,1]are optimal for 1≤p<∞.We also give the optimal Lagrange interpolation nodes when the endpoints are included in the nodes.展开更多
For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on ...For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on the direction to try the non-symmetrical continuous peak-unimodal solutions and C1 solutions.展开更多
Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P&...Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +展开更多
In this paper,we focus on the admissible transcendental meromorphic solutions of the following delay Schwarzian differential equations with rational coefficients f(z+1)-f(z-1)+a(z)S(f,z)=P(z,f(z))/Q(z,f(z)).We obtain ...In this paper,we focus on the admissible transcendental meromorphic solutions of the following delay Schwarzian differential equations with rational coefficients f(z+1)-f(z-1)+a(z)S(f,z)=P(z,f(z))/Q(z,f(z)).We obtain the necessary conditions on the degree of R(z,f)for these delay differential equations and give a classification of the delay Schwarzian differential equations according to the multiplicities of the root of Q(z,f)on f.Finally,we provide some examples to illustrate that all cases occur.展开更多
In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the e...In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations are obtained.To illustrate the ab-stract result,a concrete example is given.展开更多
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ...The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.展开更多
Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D G...Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
β-mercaptoethanol was used to induce in vitro neuronal differentiation of adipose-derived stromal cells. Within an 8-hour period post-differentiation, the induced cells exhibited typical neuronal morphology, and expr...β-mercaptoethanol was used to induce in vitro neuronal differentiation of adipose-derived stromal cells. Within an 8-hour period post-differentiation, the induced cells exhibited typical neuronal morphology, and expression of microtubule-associated protein 2 and neuron-specific enolase, which are markers of mature neurons, reached a peak at 5 hours. Specific organelle Nissl bodies of neurons were observed under transmission electron microscopy. Results of membrane potential showed that fluorescence intensity of cells was greater after 5 hours than adipose-derived stromal cells prior to induction. In addition, following stimulation with high-concentration potassium solution, fluorescence intensity increased. These experimental findings suggested that neurons differentiated from adipose-derived stromal cells and expressed mature K^＋ channels. In addition, following stimulation with high potassium solution, the membrane potential depolarized and fired an action potential, confirming that the induced cells possessed electrophysiological functions.展开更多
This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several differen...This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.展开更多
In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
文摘BACKGROUND Spinal cord injury(SCI)often results in irreversible neurological deficits;therefore,effective treatment is urgently needed.Neural stem cells(NSCs)have excellent differentiation potential.However,the role of the long noncoding RNA X inactive-specific transcript(XIST)in NSCs and SCI remains unclear.AIM To explore the role of XIST in enhancing NSC function and its therapeutic potential in SCI.METHODS We used in vitro and in vivo models to examine the effects of XIST on NSCs.XIST was overexpressed in NSCs,and its impact on mitochondrial function,neuronal differentiation,and the insulin-like growth factor 2 mRNA binding protein 2(IGF2BP2)/carnitine palmitoyl transferase 1A(CPT1A)pathway was assessed using a series of biochemical assays,quantitative PCR,and Seahorse XF24 analysis.A mouse model of SCI was used to evaluate the therapeutic effects of XIST in vivo.RESULTS Overexpression of XIST in NSCs significantly increased mitochondrial membrane potential,ATP production,and oxygen consumption rate.XIST also promoted NSC proliferation and neuronal differentiation while inhibiting astrocytic differentiation.Mechanistically,XIST regulated CPT1A expression post-transcriptionally by interacting with IGF2BP2.In vivo XIST-treated mice exhibited improved motor scores and reduced proinflammatory cytokine expression following SCI.CONCLUSIONThese findings suggested that XIST modulated mitochondrial function and neural differentiation in NSCs throughthe IGF2BP2/CPT1A pathway. While preliminary in vivo results are encouraging, further studies are needed todetermine the long-term therapeutic relevance and underlying mechanisms of XIST in SCI recovery.
基金Sponsored by 2025 Undergraduate Innovation and Entrepreneurship Training Program Project.
文摘This study focuses on the three courtyards located in the eastern,central,and western sections of the Tongzhou Campus of Renmin University of China.Adopting a functional differentiation perspective,the research systematically analyzes the patterns of plant diversity within courtyards characterized by distinct functional orientations.This analysis employs various plant species diversity indices,including the Patrick richness index,Simpson dominance index,Shannon-Wiener diversity index,and Pielou evenness index,alongside a classification of functional plant types,namely ornamental,ecological regulation,spatial shaping,and recreational assistance.The results indicate that the east courtyard presents the highest Patrick species richness(S=42),predominantly comprising spatial shaping and recreational assistance plants,which are wellsuited for recreational and passage functions.Conversely,the central courtyard exhibits the lowest Patrick species richness(S=19),characterized by a balanced distribution of functional types,with an emphasis on public display and traffic guidance.The west courtyard demonstrates the greatest stability in the tree layer(D=0.87),featuring a combination of shade-tolerant and ornamental plants that fulfill the requirements for a tranquil and naturalistic environment.One-way analysis of variance reveals that only Patrick species richness differs significantly among the courtyards(P=0.007),whereas the diversity index does not show a significant difference.This finding suggests that functional requirements precisely regulate diversity through microhabitat heterogeneity and plant configuration strategies.This study offers both a theoretical foundation and practical guidance for the plant configuration and functional optimization of small-scale courtyards on campus.
基金Anhui Provincial Natural Science Foundation(2308085QD124)Anhui Province University Natural Science Research Project(GrantNo.2023AH050918)The University Outstanding Youth Talent Support Program of Anhui Province.
文摘This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.
文摘The purpose of this paper is to add some complements to the general theory of higher-order types of asymptotic variation developed in two previous papers so as to complete our elementary (but not too much!) theory in view of applications to the theory of finite asymptotic expansions in the real domain, the asymptotic study of ordinary differential equations and the like. The main results concern: 1) a detailed study of the types of asymptotic variation of an infinite series so extending the results known for the sole power series;2) the type of asymptotic variation of a Wronskian completing the many already-published results on the asymptotic behaviors of Wronskians;3) a comparison between the two main standard approaches to the concept of “type of asymptotic variation”: via an asymptotic differential equation or an asymptotic functional equation;4) a discussion about the simple concept of logarithmic variation making explicit and completing the results which, in the literature, are hidden in a quite-complicated general theory.
基金The second named author was supported in part by an NSERC Postdoctoral Fellowship,Canada and a CR F Grant,University of Alberta
文摘This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).
文摘A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.
文摘Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.
基金Supported by the National Natural Science Foundation of China(Grant No.11871006).
文摘This paper investigates the optimal Lagrange interpolation of a class F∞of infinitely differentiable functions on[-1,1]in L_(∞)[-1,1]and weighted spaces L_(p,ω)[-1,1],1≤p<∞withωa continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation polynomials based on the zeros of polynomials with the leading coefficient 1 of the least deviation from zero in L_(p,ω)[-1,1]are optimal for 1≤p<∞.We also give the optimal Lagrange interpolation nodes when the endpoints are included in the nodes.
基金Projects supported by National Natural Science Foundation of China
文摘For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on the direction to try the non-symmetrical continuous peak-unimodal solutions and C1 solutions.
文摘Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +
基金supported by the National Natural Science Foundation of China(12201420,12231013,11701382 and 11971288)the Guangdong Basic and Applied Basic Research Foundation,China(2021A1515010054)and NCAMS.
文摘In this paper,we focus on the admissible transcendental meromorphic solutions of the following delay Schwarzian differential equations with rational coefficients f(z+1)-f(z-1)+a(z)S(f,z)=P(z,f(z))/Q(z,f(z)).We obtain the necessary conditions on the degree of R(z,f)for these delay differential equations and give a classification of the delay Schwarzian differential equations according to the multiplicities of the root of Q(z,f)on f.Finally,we provide some examples to illustrate that all cases occur.
基金Supported by the National Natural Science Foundation of China(11226337)the Science and Technology Research Projects of Henan Education Committee(22B110017).
文摘In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations are obtained.To illustrate the ab-stract result,a concrete example is given.
文摘The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.
基金The paper was financially supported by the National Natural Science Foundation of China (No. 19802008)Excellent Doctoral Dissertation Grant of the Ministry of Education of China (No. 199927)
文摘Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
文摘β-mercaptoethanol was used to induce in vitro neuronal differentiation of adipose-derived stromal cells. Within an 8-hour period post-differentiation, the induced cells exhibited typical neuronal morphology, and expression of microtubule-associated protein 2 and neuron-specific enolase, which are markers of mature neurons, reached a peak at 5 hours. Specific organelle Nissl bodies of neurons were observed under transmission electron microscopy. Results of membrane potential showed that fluorescence intensity of cells was greater after 5 hours than adipose-derived stromal cells prior to induction. In addition, following stimulation with high-concentration potassium solution, fluorescence intensity increased. These experimental findings suggested that neurons differentiated from adipose-derived stromal cells and expressed mature K^＋ channels. In addition, following stimulation with high potassium solution, the membrane potential depolarized and fired an action potential, confirming that the induced cells possessed electrophysiological functions.
基金Supported by NSFC (11001091)Chinese UniversityResearch Foundation (2010MS129)
文摘This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.
文摘In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
