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boundedness of Solutions of Quasi-periodic p-Laplacian Equations with Jumping Nonlinearity

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Acta Mathematica Sinica,English Series 2023年第1期39卷 176-192页

作者： Xin Li ZHANG Ya Qun PENG Da Xiong PIAO School of Mathematics and Physics Qingdao University of Science and TechnologyQingdao 266061P.R.China School of Mathematics(Zhuhai) Sun Yat-sen UniversityZhuhai 519082P.R.China School of Mathematical Sciences Ocean University of ChinaQingdao 266100P.R.China

In this article,we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation(φ_(p)(x’))’+aφ_(p)(x+)-bφ_(p)(x-)=g(x,t)+f(t),where g(x,t)and f(t)are quasi-periodic in t with Diophantine frequency.A new method is presented to obtain the generating function to construct canonical transformation by solving a quasi-periodic homological equation.

关键词： Quasi-periodic twist mapping invariant curve boundedness p-Laplacian

boundedness of a Derived Function of a Solution About a Class of Diffusion Variational Equations

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Acta Mathematica Sinica,English Series 2004年第3期20卷 463-474页

作者： KunHuiLIU CollegeofScience BeijingJiaotongUniversityBeijing100044P.R.China

In this paper the boundedness of a derived function of a solution about a class of diffusion variational equations is discussed. The application of it to related stochastic analysis problems is also illustrated. What should be emphasized is that the problem discussed and the ways proved in this paper are fundamentally new and the conclusion of this paper is fairly profound.

关键词： Variational equation Diffusion equation Classical solution boundedness Stochastic analysis

boundedness AND ASYMPTOTIC STABILITY OFMULTISTEP METHODS FOR GENERALIZED PANTOGRAPH EQUATIONS

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Journal of Computational Mathematics 2004年第3期22卷 447-456页

作者： Cheng-jianZhang GengSun DepartmentofMathematics HuazhongUniversityofScienceandTechnologyWuhan430074China InstituteofMathematicsandSystemsScience ChineseAcademyofScienceBeijing100080China

In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some ... 详细信息

关键词： boundedness Asymptotic stability Multistep methods Generalized pantograph equations

boundedness AND EXPONENTIAL STABILIZATION IN A PARABOLIC-ELLIPTIC KELLER–SEGEL MODEL WITH SIGNAL-DEPENDENT MOTILITIES FOR LOCAL SENSING CHEMOTAXIS

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Acta Mathematica Scientia 2022年第3期42卷 825-846页

作者： Jie JIANG Innovation Academy for Precision Measurement Science and Technology CASWuhan 430071China

In this paper we consider the initial Neumann boundary value problem for a degenerate Keller-Segel model which features a signal-dependent non-increasing motility *** main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes *** the current work,we are interested in the boundedness and exponential stability of the classical solution in higher *** the aid of a Lyapunov functional and a delicate Alikakos-Moser type iteration,we are able to establish a time-independent upper bound of the concentration provided that the motility function decreases *** we further prove the uniform-in-time boundedness of the solution by constructing an estimation involving a weighted ***,thanks to the Lyapunov functional again,we prove the exponential stabilization toward the spatially homogeneous steady *** boundedness result improves those in[1]and the exponential stabilization is obtained for the first time.

关键词： Classical solution boundedness exponential stabilization degeneracy Keller-Segel models

boundedness AND ASYMPTOTIC STABILITY IN A PREDATOR-PREY CHEMOTAXIS SYSTEM WITH INDIRECT PURSUIT-EVASION DYNAMICS

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Acta Mathematica Scientia 2022年第3期42卷 1035-1057页

作者： Shuyan QIU Chunlai MU Hong YI School of Sciences Southwest Petroleum UniversityChengdu 610500China College of Mathematics and Statistics Chongqing UniversityChongqing 401331China School of Mathematics and Statistics Chongqing Technology and Business UniversityChongqing 400067China

This work explores the predator-prey chemotaxis system with two chemicals {u_(t) = Δu + ∇ ・ (u∇v) + μ_(1)u(1 − u − α_(1)w), x ∈ Ω, t > 0,v_(t )= Δv −α_(1)v + β_(1)w, x ∈ Ω, t > 0,w_(t) = Δw − ξ∇ ・ (w∇z) + μ_(2)w(1 + α_(2)u − w), x ∈ Ω, t > 0,z_(t) =Δz −α_(2)z +β_(2)u, x ∈ Ω, t > 0, in an arbitrary smooth bounded domainΩ■R^(n) under homogeneous Neumann boundary *** parameters in the system are *** first prove that if n≤3,the corresponding initial-boundary value problem admits a unique global bounded classical solution,under the assumption thatχ,ξ,μ_(i),a_(i),α_(i) andβ_(i)(i=1,2)satisfy some suitable ***,we also analyse the asymptotic behavior of solutions to the above system and show that·when a_(1)1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system exponentially converges to(0,α_(1)/β_(1),1,0)as t→∞;·when a1=1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system polynomially converges to(0,α_(1)/β_(1),1,0)as t→∞.

关键词： Chemotaxis predator-prey boundedness stabilization

boundedness OF THE HIGHER-DIMENSIONAL QUASILINEAR CHEMOTAXIS SYSTEM WITH GENERALIZED LOGISTIC SOURCE

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Acta Mathematica Scientia 2020年第3期40卷 713-722页

作者： Qingquan TANG Qiao XIN Chunlai MU College of Mathmatics and Statistics Yili Normal UniversityYining 835000China College of Mathmatics and Statistics Chongqing UniversityChongqing 401331China

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∈***,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥***α+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.

关键词： Chemotaxis system logistic source global solution boundedness

boundedness of Solutions in Asymmetric Oscillations via the Twist Theorem

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Acta Mathematica Sinica,English Series 2001年第2期17卷 313-318页

作者： Yi Qian WANG Institute of Mathematics. Academy of Mathematics and Systems Sciences. Chinese Academy of Science, Beijing 100080 P. R. China Institute of Mathematics Academy of Mathematics and Systems Sciences Chinese Academy of Science Beijing 100080 P. R. China

In this paper we consider the boundedness of all the solutions for the equation x'+ax^+ -bx^-=f(t). where f(t) is a smooth 2π-periodic function, a and b are positive constants (a≠b).

关键词： boundedness Asymmetric Canonical transformation Twist theorem

boundedness of solutions for Duffing-type equation

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Science China Mathematics 1998年第6期41卷 595-605页

作者：袁小平 Department of Mathematics Fudan University Shanghai China

The boundedness of all solutions is shown for Duffing-type equations $\frac{{d^2 x}}{{dt^2 }} + x^{2n + 1} + \sum\limits_{j = 0}^{2n} {x^j p_j (t) = 0, n \geqslant 1,} $ wherep 1,p 2,...,p 2n are of period 1 and of Lipschitzian continuity andp n+1,...,p 2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing-type equations does not require the smoothness in the time-variable, thus answering the question posed by Dieckerhoff and Zehnder.

关键词： Duffing type equation boundedness of solution Moser’s twist theorem.

boundedness OF SOLUTIONS AND EXISTENCEOF LIMIT CYCLES FOR A NONLINEAR SYSTEMOF DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 1998年第1期18卷 113-120页

作者：黄立宏陈明博 Department of Applied Mathematics Hunan University changsha 410082 China Institute of Mathematics Academia Sinica Nankang Taipei 11529 Taiwan China

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'.

关键词： nonlinear differential system boundedness existence limit cycle