Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations

In this paper we consider a class of planar autonomous systems having an isolated limit cycle x₀ of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We consider two functions, defined by means of the eigenfunctions of the adjoint of the linearized system, and we formulate conditions in terms of them in order to have the existence of two geometrically distinct families of T-periodic solutions of the autonomous system when it is perturbed by nonsmooth T-periodic nonlinear terms of small amplitude. We also show the convergence of these periodic solutions to x₀ as the perturbation disappears and we provide an estimation of the rate of convergence. The employed methods are mainly based on the theory of topological degree and its properties that allow less regularity on the data than that required by the approach, commonly employed in the existing literature on this subject, based on various versions of the implicit function theorem.     

Periodic Solutions for a Class of Forced Lienard-type Equations

By applying the topological degree theory, we establish some sufficient conditions for the existence on T-periodic solutions for the Lienard-type equation Our results extend and improve some known results in the literature.     

LIMIT CYCLES OF A QUADRATIC HAMILTONIAN SYSTEM BY CUBIC PERTURBATIONS

In this paper,we are concerned with a cubic near-Hamiltonian system,whose unperturbed system is quadratic and has a symmetric homoclinic loop.By using the method developed in [12],we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop.Further,we give a condition under which there exist 4 limit cycles.     

Existence and uniqueness of periodic solutions for forced Liénard-type equations

By using topological degree theory and some analysis skill, some sufficient conditions for the existence and uniqueness of periodic solutions for a class of forced Lienard-type equations are obtained.     

一类平面三次微分系统极限环的存在性与唯一性

蛤出三次系统{dx/dt=-y(ax^2 bx 1) δx-lx^2 dy/dt=x(ax^2 bx 1)极限环的不存在性，存在性及唯一性的一些充分条件．     

具有功能反应的两斑块扩散时滞竞争系统正周期解的存在性

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｍａｎｙｓｐｅｃｉｅｓｔｈｅｓｐａｔｉａｌｆａｃｔｏｒｓａｒｅｉｍｐｏｒｔａｎｔｉｎｐｏｐｕｌａｔｉｏｎｄｙｎａｍｉｃｓ .Ｔｈｅｔｈｅｏｒｅｔｉｃａｌｓｔｕｄｙｏｆｓｐａｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｉｎｍａｎｙｐａｐｅｒｓ .Ｍｏｓｔｏｆｔｈｅｐｒｅｖｉｏｕｓｐａｐｅｒｓｆｏｃｕｓｅｄｏｎｔｈｅｃｏｅｘｉｓｔｅｎｃｅｏｆｐｏｐｕｌａｔｉｏｎｓｍｏｄｅｌｌｅｄｂｙｓｔｓｔｅｍｓｏｆｏｒｄｉｎａｒｙｄｉｆｆｅｒｅ…     

PERIODIC SOLUTIONS FOR NEUTRAL LINARD EQUATION WITH A STATEMENT-DEPENDENT DEVIATION VARIABLE

Using the theroy of topological degree, the paper studies the periodic solutions to a type of neutral Lienard equation with state-dependent deviation variable. A sufficient condition for the existence of periodic solution is obtained.     

EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A DELAYED PERIODIC PREDATOR-PREY MODEL OF IVLEV TYPE

A periodic coefficients predator-prey system of Ivlev type with both discrete and continuous time delay is investigated. A sufficient condition of the existence of positive periodic solution is established for the system by using the continuation theorem of coincidence degree theory.     

一类多滞量周期扰动非线性系统的周期解

研究一类具有多个滞量的周期扰动非线性系统的T周期解.利用拓扑度的方法得到了系统存在T周期解的充分条件.作为应用,证明了具有滞后的单种群对数模型在一定条件下存在正周期解.     

二阶非线性变系数奇异微分方程的周期解

利用拓扑度理论和不动点指数理论,研究了二阶非线性变系数奇异微分方程u″(t)+a(t)u(t)=r(t)f(u(t))的周期解的存在性.特别地,本文没有假设a(t)和f(u)的非负性.     

Relative Superlinearity Implies Infinitely Many Solutions to Sturm-Liouville BVPs with Laplacian Type Operators

By the use of continuation theorems and the duality principle it＇s proved that for both homogeneous and nonhomogeneous Sturm-Liouville boundary value problems with Laplacian type operators, relative superlinearity implies the existence of infinitely many solutions under a few weakly added conditions.     

时滞Rayleigh方程周期解问题

利用Mahwin重合度拓展定理研究了一类具时滞Rayleigh方程x″(t)+f(x′(t))+g∫0-rx(t+s)dm(s)=p(t)周期解问题,得到了周期解存在的一组充分条件.     

LIMIT CYCLES AND CENTER-FOCUS OF NONLINEAR SYSTEMS

The authors consider the nonhnear systems x=h(y)-F(x),y=-g(x) in which g(x) may be not differentiabte and the system can be nonsymmetric. Some conditions which en-sure that there exists an infinite number of limit cycles are obtained. A problem about center-focus put forward by R. Conti has been answered.     

偏差变元的二阶n-维p-Laplacian方程调和解的存在性

本文研究了一类具偏差变元的二阶n-维p-Laplacian方程调和解的存在性,在对阻尼项不作限制的前提下,利用拓扑度理论得到了存在调和解的新条件,改进了一些已有的结果.     

一类二阶迭代微分方程的周期解

利用拓扑度理论研究了一类二阶迭代泛函微分方程x(t) g(x(x(t)))=f(t,x(t),x(t))的周期解的存在性,得出了周期解存在的充分条件.