The Global Navigation Satellite System(GNSS)has been widely adopted in numerous fields,including intelligent transportation,remote sensing,and aeronautical and astronautical engineering.As new navigation approaches,te...The Global Navigation Satellite System(GNSS)has been widely adopted in numerous fields,including intelligent transportation,remote sensing,and aeronautical and astronautical engineering.As new navigation approaches,technologies,and applications continue to emerge,they attract significant global attention.Ensuring reliable positioning solutions with high accuracy,strong anti-interference capabilities,high availability and low integrity risks has become increasingly critical.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div...In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div(|∇u|^(p-2)∇u),p^(*)=3p/3-p,V:R^(3)→R is a potential function with a local minimum and f is subcritical growth.Based on the penalization method,Nehari manifold techniques and Ljusternik-Schnirelmann category theory,we obtain the multiplicity and concentration of positive solutions to the above system.展开更多
This study presents a novel analytical algorithm for solving the forward position problem of a triangular platform Stewart-type parallel robot(STPR).By introducing a virtual chain and leveraging tetrahedral geometric ...This study presents a novel analytical algorithm for solving the forward position problem of a triangular platform Stewart-type parallel robot(STPR).By introducing a virtual chain and leveraging tetrahedral geometric principles,the proposed method derives analytical solutions for the position and orientation of the moving platform.The algorithm systematically addresses the nonlinearity inherent in the kinematic equations of parallel mechanisms,providing explicit expressions for the coordinates of key moving attachment points.Furthermore,the methodology is extended to general triangular platform STPRs with non-coplanar fixed attachments.Numerical validation through virtual experiments confirms the accuracy of the solutions,demonstrating that the mechanism admits eight distinct configurations for a given set of limb lengths.The results align with established kinematic principles and offer a computationally efficient alternative to iterative analytical approaches,contributing to the advancement of precision control in parallel robotic systems.展开更多
In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p...In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p≤q<p^(3)=3p/3-p and △_(p)u=div(|▽u|^(p-2)▽u)Under certain assumptions on the functions l and h, we employ the mountain pass theorem to establish the existence of positive solutions for this system.展开更多
In this work,we demonstrate that the existence of an Z-shaped connected component within the set of positive solutions for the one-dimensional prescribed mean curvature equation in Minkowski space■with boundary condi...In this work,we demonstrate that the existence of an Z-shaped connected component within the set of positive solutions for the one-dimensional prescribed mean curvature equation in Minkowski space■with boundary conditions having parameter in two cases f(O)=0 and f(0)>0 by using upper and lower solution method,where λ>0 is a parameter,f∈C^(2)([0,∞),R)is monotonically increasing and lim_(μ→1)^(f(u)/1-u=0,h∈C^(1)([0,1],(0,∞))is a nonincreasing function and h(t)>1.展开更多
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation b...This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.展开更多
In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value pr...In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals■where Δu(x)=u(x+1)-u(x)is the forward difference operator,■is continuous,a>0,B and C are nonnegative constants.展开更多
We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global min...We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive de...The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.展开更多
We prove the existence of a positive solution to the problem-Δu=a(x)f(u), x∈Ω, u(x)=0,x∈Ω,where Ω is a bounded domain in R n with smooth boundary, a(x) is allowed to change sign.
The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which e...The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.展开更多
In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam wh...In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.展开更多
The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0...The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.展开更多
Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some i...Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.展开更多
This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive...This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.展开更多
Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of ...Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.展开更多
文摘The Global Navigation Satellite System(GNSS)has been widely adopted in numerous fields,including intelligent transportation,remote sensing,and aeronautical and astronautical engineering.As new navigation approaches,technologies,and applications continue to emerge,they attract significant global attention.Ensuring reliable positioning solutions with high accuracy,strong anti-interference capabilities,high availability and low integrity risks has become increasingly critical.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
基金supported by the Natural Science Foundation of Gansu Province(No.24JRRP001)。
文摘In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div(|∇u|^(p-2)∇u),p^(*)=3p/3-p,V:R^(3)→R is a potential function with a local minimum and f is subcritical growth.Based on the penalization method,Nehari manifold techniques and Ljusternik-Schnirelmann category theory,we obtain the multiplicity and concentration of positive solutions to the above system.
基金supported by the Opening Project of State Key Laboratory of Mechanical Transmission for Advanced Equipment(No.SKLMT-MSKFKT202330)the National Natural Science Foundation of China(No.52575022)the Jiangsu Province Postgraduate Research&Practice Innovation Program(No.KYCX25_1403)。
文摘This study presents a novel analytical algorithm for solving the forward position problem of a triangular platform Stewart-type parallel robot(STPR).By introducing a virtual chain and leveraging tetrahedral geometric principles,the proposed method derives analytical solutions for the position and orientation of the moving platform.The algorithm systematically addresses the nonlinearity inherent in the kinematic equations of parallel mechanisms,providing explicit expressions for the coordinates of key moving attachment points.Furthermore,the methodology is extended to general triangular platform STPRs with non-coplanar fixed attachments.Numerical validation through virtual experiments confirms the accuracy of the solutions,demonstrating that the mechanism admits eight distinct configurations for a given set of limb lengths.The results align with established kinematic principles and offer a computationally efficient alternative to iterative analytical approaches,contributing to the advancement of precision control in parallel robotic systems.
文摘In this paper,we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent {-△_(p)u+|u|^(p-2)u=|u|^p^(*-2)u+ph(x)|u|^(q-2)u in R^(3),-△Φt(x)|u|^(p) in R^(3) where μ>0,3/2<p<3,p≤q<p^(3)=3p/3-p and △_(p)u=div(|▽u|^(p-2)▽u)Under certain assumptions on the functions l and h, we employ the mountain pass theorem to establish the existence of positive solutions for this system.
基金Supported by the National Natural Science Foundation of China(12361040)。
文摘In this work,we demonstrate that the existence of an Z-shaped connected component within the set of positive solutions for the one-dimensional prescribed mean curvature equation in Minkowski space■with boundary conditions having parameter in two cases f(O)=0 and f(0)>0 by using upper and lower solution method,where λ>0 is a parameter,f∈C^(2)([0,∞),R)is monotonically increasing and lim_(μ→1)^(f(u)/1-u=0,h∈C^(1)([0,1],(0,∞))is a nonincreasing function and h(t)>1.
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金Supported by Research Start-up Fund of Jianghan University(06050001).
文摘This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.
基金Supported by the National Natural Science Foundation of China(Grant No.12361040)the Department of Education University Innovation Fund of Gansu Province(Grant No.2021A-006)。
文摘In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals■where Δu(x)=u(x+1)-u(x)is the forward difference operator,■is continuous,a>0,B and C are nonnegative constants.
文摘We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.
文摘We prove the existence of a positive solution to the problem-Δu=a(x)f(u), x∈Ω, u(x)=0,x∈Ω,where Ω is a bounded domain in R n with smooth boundary, a(x) is allowed to change sign.
文摘The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.
文摘In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.
文摘The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.
文摘Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.
文摘This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.
文摘Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
