一类超线性Hill型对称碰撞方程的周期运动

本文考虑一类超线性Hill型对称碰撞方程的对称碰撞周期解的存在性、重性和分布问题.通过坐标变换的方法把碰撞相平面转化为全平面进行研究,在一类关于时间映射的超线性条件下证明有外力方程无穷多个对称碰撞调和解和对称碰撞次调和解的存在性;同时研究在没有外力时方程的对称碰撞周期解的稠密性分布.本文还给出对称碰撞方程对称碰撞周期解存在的充分条件.     

奇异超线性半正定二阶周期边值问题的正解

基于格林函数理论,主要利用Lerray-Schauder抉择定理和上下解方法针对半正定条件下,奇异超线性二阶周期边值问题正解的存在性进行推理证明,获取了奇异超线性二阶周期边值问题的一个正解.     

Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces

The existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper. Our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of Leray-Schauder type and on a fixed point theorem in cones.     

一类二阶Hamiltonian系统的无穷多周期解

研究一类超线性二阶Hamiltonian系统,且非线性项是奇的,不需要假设Ambros-etti-Rabinowitz的超二次条件,利用对称型山路引理得到无穷多周期解存在性结果.     

电报方程双周期解的极大值原理与强正性估计及应用

本文讨论非线性电报方程u_(tt)-u_(xx)+cu_t=F(t,x,u),(t,x)∈R~2时空双2π周期解的存在性。改进了Ortega与Robles-Perez关于线性电报方程双周期解的极大值原理,应用新获得的极大值原理,推广了相应的上下解定理,并且加强了极大值原理的结论,建立了线性方程解的强正性估计,利用这个强正性估计及锥上的不动点定理获得了超线性电报方程及奇异电报方程正双周期解的存在性。     

Ground state solutions for asymptotically periodic Schrödinger equations with indefinite linear part

Using the method of the Nehari manifold, we study the existence of ground state solutions for asymptotically periodic Schrödinger equations with indefinite linear part and superlinear nonlinearity. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence of periodic and subharmonic solutions for second-order superlinear difference equations

By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations△2xn-1+f(n,xn)=0some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinityin z.     

Homoclinic solutions in periodic difference equations with mixed nonlinearities

In this paper, by using critical point theory in combination with periodic approximations, we obtain some new sufficient conditions on the nonexistence and existence of homoclinic solutions for a class of periodic difference equations. Unlike the existing literatures that always assume that the nonlinear terms are only either superlinear or asymptotically linear at , but superlinear at 0, our nonlinear term can mix superlinear nonlinearities with asymptotically linear ones at both and 0. To the best of our knowledge, this is the first time to consider the homoclinic solutions of this class of difference equations with mixed nonlinearities. Our results are necessary in some sense, and extend and improve some existing ones even for some special cases. Copyright © 2015 John Wiley & Sons, Ltd.     

Existence of solutions for sub-linear or super-linear operator equations

We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci and Rabinowitz are special cases of the theorems.     

具有阶段结构且食饵有避难所的模型分析

研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

Multiplicity of positive periodic solutions to superlinear repulsive singular equations

In this paper, we study positive periodic solutions to the repulsive singular perturbations of the Hill equations. It is proved that such a perturbation problem has at least two positive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbation is superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.     

R~N中带周期位势的超线性p-Laplacian方程的无穷多解

在非线性项f是关于u的奇函数,势函数是有界的周期函数且下界是正的,Sobolev嵌入缺乏了紧性和f不再满足（AR）条件下,运用临界点理论中的喷泉定理和集中紧性原则证明了R~N中具有周期势函数的一类超线性p-Laplacian方程存在无穷多非平凡解。     

一类具第三类功能反应且食饵具有避难所的捕食系统的分析

研究了一类具第三类功能反应且食饵具有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下,系统存在全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

二阶微分系统奇异正定超线性周期边值问题的多重正解

主要研究了二阶微分系统具有奇异正定超线性周期边值问题多重正解的存在性问题,利用Leray-Schauder抉择定理和锥不动点定理给出了奇异正定超线性周期边值问题-(p(t)x′)′+q1(t)x=f1(t,x,y),t∈I=[0,1]-(p(t)y′)′+q2(t)y=f2(t,x,y)x(0)=x(1),x[1](0)=x[1](1)y(0)=y(1),y[1](0)=y[1](1)(1.1)的多重正解的存在性,其中非线性项fi(t,x,y)(i=1,2)在x=∞,y=∞点处超线性,在(x,y)=(0,0)处具有奇性.这里定义x[1](t)=p(t)x′(t),y[1](t)=p(t)y′(t)为准导数,其中系数p(t),qi(t)(i=1,2)是定义在[0,1]上的可测函数,且p(t)>0,qi(t)>0(i=1,2),a.e[0,1],fi(t,x,y)∈C(I×R×R,R+),R+=(0,+∞).     

Periodic Solutions of Second Order Superlinear Singular Dynamical Systems

We study the existence of periodic solutions of second order superlinear dynamical systems with a singularity of repulsive type. The proof is based on a well-known fixed point theorem for completely continuous operators. We do not need to consider so-called strong force conditions. Recent results in the literature are generalized and significantly improved.     

具无穷时滞的中立型周期微分系统周期解的存在性

研究了一类具无穷时滞的中立型周期微分系统周期解的存在性问题.利用指数型二分性及Krasnoselskii不动点定理,建立了保证该系统的周期解的存在性的充分条件.所得结果推广了文[1-7]的有关结果.     

非自治Ginzburg-Landau方程的周期解和全局周期吸引子

研究受周期外力影响的非自治Ginzburg-Landau方程的解的长时间行为.首先证明系统在空间H上存在周期解,而且周期解包含在空间V中的一个有界吸收集内.然后证明了当耗散系数λ满足一定条件时,该系统在空间H上具有唯一的周期解,该周期解指数吸引H中的任意有界集.     

无穷时滞Liénard方程的周期解

讨论具有无穷时滞Liénard型方程x+э2F(x)/эx2x+g(t,xt)=p(t)的周期解问题,利用重合度理论得到了周期解存在的充分条件.     

分数阶微分方程的一些新结果

第一部分,介绍分数阶导数的定义和著名的Mittag—Leffler函数的性质．第二部分,利用单调迭代方法给出了具有2序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性和唯一性．第三部分,利用上下解方法和Schauder不动点定理给出了具有2序列Riemann—Liouville分数阶导数微分方程周期边值问题解的存在性．第四部分,利用Leray—Schauder不动点定理和Banach压缩映像原理建立了具有n序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性、唯一性和解对初值的连续依赖性．第五部分,利用锥上的不动点定理给出了具有Caputo分数阶导数微分方程边值问题,在超线性（次线性）条件下C310,11正解存在的充分必要条件．最后一部分,通过建立比较定理和利用单调迭代方法给出了具有Caputo分数阶导数脉冲微分方程周期边值问题最大解和最小解的存在性．     

Multibump solutions for discrete periodic nonlinear Schrödinger equations

In this paper, we study the existence of multibump solutions for discrete nonlinear Schrödinger equations with periodic potentials. We first reduce the existence of multibump homoclinic solutions to the existence of an isolated homoclinic solution with a nontrivial critical group. Then, we study the existence of homoclinics with nontrivial critical groups for both superlinear and asymptotically linear discrete periodic nonlinear Schrödinger equations, and we provide simple sufficient conditions for the existence of homoclinics with nontrivial critical groups in the positive definite case. As an application, we get, without any symmetry assumptions, infinitely many geometrically distinct homoclinic solutions with exponential decay at infinity.