| 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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| 引用本文： | 王在洪.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[J].数学年刊A辑(中文版),2003(1). |
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| 作者姓名： | 王在洪 |
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| 作者单位： | 首都师范大学数学系 北京 |
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| 基金项目： | 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 |
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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.
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| 关 键 词： | 跳跃非线性项 Fucik谱曲线 周期解 |
THE EXISTENCE OF PERIODIC SOLUTIONS OF THE SECOND ORDER DIFFERENTIAL EQUATIONS WITH JUMPING NONLINEARITIES DEPENDING ON THE DERIVATIVES |
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| WANG Zaihong.THE EXISTENCE OF PERIODIC SOLUTIONS OF THE SECOND ORDER DIFFERENTIAL EQUATIONS WITH JUMPING NONLINEARITIES DEPENDING ON THE DERIVATIVES[J].Chinese Annals of Mathematics,2003(1). |
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| Authors: | WANG Zaihong |
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| Institution: | WANG Zaihong Department of Mathematics,Capital Normal University,Beijing 100037,China. |
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| Abstract: | 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. |
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| Keywords: | Jumping nonlinearity Fucik spectrum Periodic solution |
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