This paper deals with the global boundedness of a two-competing-species chemotaxis model with indirect signal production in a three-dimensional bounded domain.The current work extends prior results by ZHENG et al.(202...This paper deals with the global boundedness of a two-competing-species chemotaxis model with indirect signal production in a three-dimensional bounded domain.The current work extends prior results by ZHENG et al.(2022)who established global existence and boundedness of classical solution under the parameter constraintsµ_(1)µ_(2)a_(2)≥χ1(4+µ_(2)^(2)a _(2)^(2)),µ_(1)µ_(2)a_(1)≥χ2(4+µ_(1)^(2)a_(1)^( 2)).Our main contribution demonstrates that these technical conditions can be significantly relaxed toµ1≥5χ_(1),µ2≥5χ_(2),thereby expanding the admissible parameter space for solution boundedness.展开更多
For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case ...For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.展开更多
In this paper,we utilize the theory of Kurzweil-Henstock integrals to investigate new criteria for boundedness in terms of two measures for generalized ordinary differential equations.As applications,we establish crit...In this paper,we utilize the theory of Kurzweil-Henstock integrals to investigate new criteria for boundedness in terms of two measures for generalized ordinary differential equations.As applications,we establish criteria for(h_(0),h)-uniform boundedness and(h_(0),h)-uniform ultimate boundedness in terms of two measures for impulsive differential equations.展开更多
This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution un...This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution under some conditions.展开更多
In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forci...In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forcing function andαis a real parameter.Inspired by this special discontinuous oscillator,we study a more general discontinuous oscillator x′′+ω^(2)x+ϕ(x)=p(t),whereω∈R^(+)\N andϕ(x)has one discontinuous point.We show that every solution of this general discontinuous oscillator is bounded when some conditions are satisfied.展开更多
The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently ...The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H_(∞) finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.展开更多
In this paper,we study the dynamic behavior of the following system of coupled forced asymmetric oscillations{(φp1(x'1))'+a1φp1(x+1)-b1φp1(x-1)+φ1(x2)=f1(t),(φp2(x'2))'+a2φp2(x+2)-b2φp2(x-2)+φ2...In this paper,we study the dynamic behavior of the following system of coupled forced asymmetric oscillations{(φp1(x'1))'+a1φp1(x+1)-b1φp1(x-1)+φ1(x2)=f1(t),(φp2(x'2))'+a2φp2(x+2)-b2φp2(x-2)+φ2(x1)=f2(t),where for i=1,2,φpi(u)=|u|pi-2u,pi≥2,x+i=max{xi,0},x-i=max{-xi,0},ai and bi are two different positive constants,φi:R→R is continuous and bounded,fi(t)is a real analytic quasi-periodic function with the frequencyω=(ω1,ω2,…,ωn)and is even in t.We will discuss the existence of quasi-periodic solutions and the boundedness of all solutions for the aforementioned system of coupled forced asymmetric oscillations.展开更多
Due to the centralization of charging stations(CSs),CSs are organized as charging station alliances(CSAs)in the commercial competition.Under this situation,this paper studies the profit-oriented dynamic pricing strate...Due to the centralization of charging stations(CSs),CSs are organized as charging station alliances(CSAs)in the commercial competition.Under this situation,this paper studies the profit-oriented dynamic pricing strategy of CSAs.As the practicability basis,a privacy-protected bidirectional real-time information interaction framework is designed,under which the status of EVs is utilized as the reference for pricing,and the prices of CSs are the reference for charging decisions.Based on this framework,the decision-making models of EVs and CSs are established,in which the uncertainty caused by the information asymmetry between EVs and CSs and the bounded rationality of EV users are integrated.To solve the pricing decision model,the evolutionary game theory is adopted to describe the dynamic pricing game among CSAs,the equilibrium of which gives the optimal pricing strategy.Finally,the case study conducted in an urban area of Shanghai,China,validates the practicability of the framework and the effectiveness of the dynamic pricing strategy.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.
In this paper, author obtain sufficient conditions for the boundedness of solutions and the existence of limit cycles of the nonlinear differential system dx/dt = p(y), dy/dt = -q(y)h(x,y) - g(x) without the tradition...In this paper, author obtain sufficient conditions for the boundedness of solutions and the existence of limit cycles of the nonlinear differential system dx/dt = p(y), dy/dt = -q(y)h(x,y) - g(x) without the traditional assumptions 'h(x,y) greater than or equal to 0 for \x\ sufficiently large' and 'integral(0)(+/-infinity) g(x)dx = +infinity'.展开更多
This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),...This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.展开更多
基金Supported by the National Natural Science Foundation of China(12301631)the Natural Science Foundation of Qinghai Province(2023-ZJ-949Q)。
文摘This paper deals with the global boundedness of a two-competing-species chemotaxis model with indirect signal production in a three-dimensional bounded domain.The current work extends prior results by ZHENG et al.(2022)who established global existence and boundedness of classical solution under the parameter constraintsµ_(1)µ_(2)a_(2)≥χ1(4+µ_(2)^(2)a _(2)^(2)),µ_(1)µ_(2)a_(1)≥χ2(4+µ_(1)^(2)a_(1)^( 2)).Our main contribution demonstrates that these technical conditions can be significantly relaxed toµ1≥5χ_(1),µ2≥5χ_(2),thereby expanding the admissible parameter space for solution boundedness.
基金partially supported by the research grant of Macao University of Science and Technology(FRG-22-075-MCMS)the Macao Government Research Funding(FDCT0128/2022/A)+2 种基金the Science and Technology Development Fund of Macao SAR(005/2022/ALC)the Science and Technology Development Fund of Macao SAR(0045/2021/A)Macao University of Science and Technology(FRG-20-021-MISE)。
文摘For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.
基金supported by the Natural Science Foundation of Zhejiang Province(No.LY19A010013)。
文摘In this paper,we utilize the theory of Kurzweil-Henstock integrals to investigate new criteria for boundedness in terms of two measures for generalized ordinary differential equations.As applications,we establish criteria for(h_(0),h)-uniform boundedness and(h_(0),h)-uniform ultimate boundedness in terms of two measures for impulsive differential equations.
基金Supported by the National Natural Science Foundation of China(11301419)the Research and innovation Team of China West Normal University(CXTD2020-5)。
文摘This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution under some conditions.
基金Supported by Key Research Funds for the Universities of Henan Province(Grant No.19A110018)Foundation for Key Teacher of Henan Polytechnic University(Grant No.2022XQG-09).
文摘In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forcing function andαis a real parameter.Inspired by this special discontinuous oscillator,we study a more general discontinuous oscillator x′′+ω^(2)x+ϕ(x)=p(t),whereω∈R^(+)\N andϕ(x)has one discontinuous point.We show that every solution of this general discontinuous oscillator is bounded when some conditions are satisfied.
基金supported by the National Nature Science Foundation of China (61877028, 61773015).
文摘The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H_(∞) finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1226101411901131)the In-novative Exploration and Academic Seedling Project of Guizhou University of Finance and Economics(Grant No.2024XSXMA07).
文摘In this paper,we study the dynamic behavior of the following system of coupled forced asymmetric oscillations{(φp1(x'1))'+a1φp1(x+1)-b1φp1(x-1)+φ1(x2)=f1(t),(φp2(x'2))'+a2φp2(x+2)-b2φp2(x-2)+φ2(x1)=f2(t),where for i=1,2,φpi(u)=|u|pi-2u,pi≥2,x+i=max{xi,0},x-i=max{-xi,0},ai and bi are two different positive constants,φi:R→R is continuous and bounded,fi(t)is a real analytic quasi-periodic function with the frequencyω=(ω1,ω2,…,ωn)and is even in t.We will discuss the existence of quasi-periodic solutions and the boundedness of all solutions for the aforementioned system of coupled forced asymmetric oscillations.
基金sponsored in part by the National Natural Science Foundation of China(52167014)in part by the Science and Technology Commission of Shanghai Municipality(23XD1422000,23QB1400500).
文摘Due to the centralization of charging stations(CSs),CSs are organized as charging station alliances(CSAs)in the commercial competition.Under this situation,this paper studies the profit-oriented dynamic pricing strategy of CSAs.As the practicability basis,a privacy-protected bidirectional real-time information interaction framework is designed,under which the status of EVs is utilized as the reference for pricing,and the prices of CSs are the reference for charging decisions.Based on this framework,the decision-making models of EVs and CSs are established,in which the uncertainty caused by the information asymmetry between EVs and CSs and the bounded rationality of EV users are integrated.To solve the pricing decision model,the evolutionary game theory is adopted to describe the dynamic pricing game among CSAs,the equilibrium of which gives the optimal pricing strategy.Finally,the case study conducted in an urban area of Shanghai,China,validates the practicability of the framework and the effectiveness of the dynamic pricing strategy.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
文摘Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.
文摘In this paper, author obtain sufficient conditions for the boundedness of solutions and the existence of limit cycles of the nonlinear differential system dx/dt = p(y), dy/dt = -q(y)h(x,y) - g(x) without the traditional assumptions 'h(x,y) greater than or equal to 0 for \x\ sufficiently large' and 'integral(0)(+/-infinity) g(x)dx = +infinity'.
基金This work is supported by the Youth Doctor Science and Technology Talent Training Project of Xinjiang Uygur Autonomous Region(2017Q087).
文摘This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.
