跳跃非线性项依赖于导数的二阶微分方程周期解的存在性

THE EXISTENCE OF PERIODIC SOLUTIONS OF THE SECOND ORDER DIFFERENTIAL EQUATIONS WITH JUMPING NONLINEARITIES DEPENDING ON THE DERIVATIVES

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摘要本文研究二阶微分方程χ"+aχ+-bχ-+f(χ)g(χ'=p(t)周期解的存在性,这里χ+=max{χ,0},χ-=max{-χ,0},a,6是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(χ)的极限lim.g(χ)=g(+∞),lim g(χ)=g(-∞)和f(χ)的极限lim,g(χ)=f(+∞),lim f(χ)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件. In this paper, we study the existence of periodic solutions of equationwhere (a, 6) lies on some Fucik spectrum curve. We provide sufficient conditions for the existence of periodic solutions for this equation if limits limand lim lim exist and are finite.

作者王在洪

机构地区首都师范大学数学系

出处《数学年刊（A辑）》 CSCD 北大核心 2003年第1期47-58,共12页 Chinese Annals of Mathematics

基金国家自然科学基金(No.10001025) 北京市自然科学基金(No.1022003)资助的项目

关键词跳跃非线性项 Fucik谱曲线周期解二阶微分方程 Jumping nonlinearity, Fucik spectrum, Periodic solution

分类号 O175.12 [理学—基础数学]

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数学年刊（A辑）

2003年第1期

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跳跃非线性项依赖于导数的二阶微分方程周期解的存在性

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