MULTIPLE PERIODIC SOLUTIONS TO SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH INFINITE DELAY

This paper is concerned with the existence of positive periodic solutions to a second order functional differential equation with infinite delay.Under the appropriate conditions,some existence and multiplicity of positive periodic solutions are derived by an abstract fixed-point theorem.     

二阶非线性常微分方程的正周期解

本文应用Ｋｒａｓｎｏｓｅｌｓｋｉｉ锥映射不动点定理，研究了二阶非线性常微分方程的ω-周期解的存在性，获得了若干正ω-周期解的存在性与多重性结果．     

二阶无穷时滞泛函微分方程的正周期解

应用Krasnoselskii不动点定理讨论二阶无穷时滞泛函微分方程(t)+a(t)x(t)=f(t,xt)的正ω-周期解的存在性.     

Periodic solutions of singular second order equations at resonance

In this paper, we study the existence of positive periodic solutions for singular second order equations x" + n²/4x+h(x) = p(t), where h has a singularity at the origin and n is a positive integer. We give an explicit condition to ensure the existence of positive periodic solutions when h is an unbounded perturbation at infinity by using qualitative analysis and topological degree theory.     

时间标度上的动态方程周期边值问题的正解

讨论了时间标度上一类二阶非线性动态方程的周期边值问题正解以及多解的存在性,利用锥上的不动点理论给出了简捷的判别方法并举例。     

Positive solutions of a nonlinear impulsive equation with periodic boundary conditions

In this paper, we investigate nonlinear second order differential equations subject to linear impulse conditions and periodic boundary conditions. Sign properties of an associated Green’s function are exploited to get existence results for positive solutions of the nonlinear boundary value problem with impulse. Upper and lower bounds for positive solutions are also given. The results obtained yield periodic positive solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.     

Almost Periodic Solutions of Nonlinear Second Order Differential Equations

We provide existence results for almost periodic solutions of nonlinear second order ordinary differential equations. The results extend existence results for periodic solutions of periodic equations, where the existence of periodic sub and supersolutions implied the existence of periodic solutions.     

一类具有无穷多个周期解的二阶偏微分方程

本文首先给出了一类具有无穷多个周期解的无阻尼二阶线性偏微分方程所描述的系统。同时讨论了一类无阻尼非线性二阶偏微分方程存在多个周期解的情况，最后给出了一个判断有阻尼二阶偏微分系统存在周期解的方法。     

Existence of Multiple Positive Perio dic Solutions for Second Order Differential Equations

In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′(t) + p(t)x′(t) + q(t)x(t) = f(t, x(t)).By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.     

Positive Periodic Solutions of Systems of Second Order Ordinary Differential Equations

We establish the existence, multiplicity and nonexistence of positive periodic solutions of systems of second order ordinary differential equations.     

零点指数的计算及其对二阶周期边值问题的应用

利用锥理论,给出有关零点指数计算的新方法.作为应用,考虑了二阶周期边值问题正解的存在性.     

Periodic solutions of second order nonlinear difference equations with discrete -Laplacian

We use Brouwer degree to prove existence and multiplicity results for the periodic solutions of some nonlinear second order difference equations involving discrete -Laplacian. We obtain in particular upper and lower solutions theorems, Ambrosetti–Prodi type multiplicity results, sharp existence conditions for nonlinearities which are bounded from below or from above and necessary and sufficient conditions for the existence of positive periodic solutions when the nonlinearity is singular at 0.     

On existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations

The existence and multiplicity of positive solutions are established to periodic boundary value problems for singular nonlinear second order ordinary differential equations. The arguments are based only upon the positivity of the Green's functions and the Krasnosel'skii fixed point theorem. As an example, a periodic boundary value problem is also considered which comes from the theory of nonlinear elasticity.     

Multiple periodic solutions for Hamiltonian systems with not coercive potential

Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems.     

Existence of periodic and subharmonic solutions for second order functional difference equations

In this paper, by using the critical point theory, the existence of periodic and subharmonic solutions to a class of second order functional difference equations is obtained. The main approach used in our paper is variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic and subharmonic solutions of second order forward and backward difference equations.     

奇异一阶周期系统的多重正解

主要建立了奇异一阶周期系统的多重正解,证明了在适当的条件下这个问题至少存在两个解.第一个正解的存在性是利用非线性L eray-Schauder抉择定理得到的,第二个解是利用K rasnoselsk ii锥不动点定理得到的.     

Four positive periodic solutions for the first order differential system

In this paper, we establish the existence of four positive periodic solutions for the first order differential system by using the continuation theorem of coincidence degree theory. When our result is applied to a competition Lotka-Volterra population model, we obtain the existence of four positive periodic solutions for this model.     

Positive solutions of even order system periodic boundary value problems

We study a class of even order system boundary value problems with periodic boundary conditions. A series of criteria are obtained for the existence of one, two, any arbitrary number, and even a countably infinite number of positive solutions. Criteria for the nonexistence of positive solutions are also derived. As for the second order case, our results extend, improve, and supplement those in the literature for scalar and system boundary value problems. Several examples are given to demonstrate the applications. Moreover, we obtain conditions for system periodic boundary value problems of a different form to have nontrivial solutions by transforming our main results to such problems.     

Periodic solutions of second order non-autonomous singular dynamical systems

In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray-Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder's fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions. Recent results in the literature are generalized and significantly improved.     

具无穷时滞高阶中立型微分方程的周期解

利用重合度理论研究了一类具有无穷时滞高阶中立型泛函微分方程周期解的存在性,获得了该方程存在周期解的充分条件,推广和改进了二阶方程的相应结果.