MULTIPLICITY RESULTS FOR PERIODIC SOLUTIONS TO A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS

Guo ZM; Zhang XM

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MULTIPLICITY RESULTS FOR PERIODIC SOLUTIONS TO A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS

机译：一类二阶时滞微分方程的周期解的多重性结果

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摘要

In this paper, we study the following second order delay differential equation x ''(t) - - f(x(t), x(t - tau)). When f possesses a symmetric property and grows asymptotically linear both at zero and at infinity, some new results for the existence and multiplicity of periodic solutions are obtained by using the critical point theory and S-1 geometrical index theory.

机译：在本文中，我们研究以下二阶延迟微分方程x''（t）--f（x（t），x（t-tau））。当f具有对称性质并且在零和无穷大处渐近线性增长时，使用临界点理论和S-1几何指数理论可获得有关周期解的存在性和多重性的一些新结果。

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《Communications on pure and applied analysis》 |2010年第6期|共14页
作者
Guo ZM; Zhang XM;
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正文语种 eng
中图分类数学;
关键词
Second order delay differential equations; multiple periodic solutions; Hamiltonian systems; critical point theory; S-1 geometrical index theory CRITICAL-POINT THEORY; HAMILTONIAN-SYSTEMS;

机译：二阶时滞微分方程;多个周期解;哈密顿系统;临界点理论;S-1几何指标理论;临界点理论;哈密尔顿系统;

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1. Multiplicity results of periodic solutions for a class of first order delay differential equations [J] . Wu K., Wu X. Journal of Mathematical Analysis and Applications . 2012,第2期

机译：一类一阶时滞微分方程周期解的多重性结果
2. MULTIPLICITY RESULTS ON PERIODIC SOLUTIONS TO HIGHER-DIMENSIONAL DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS [J] . Zheng Bo, Guo Zhiming The Rocky Mountain journal of mathematics . 2014,第5期

机译：具有多个时滞的高维微分方程周期解的多重性结果
3. Multiplicity of periodic solutions to symmetric delay differential equations [J] . Krawcewicz W., Yu J., Xiao H. Journal of fixed point theory and applications . 2013,第1期

机译：对称时滞微分方程的周期解的多重性
4. Computation of Maslov-Type Index and Periodic Solutions for a Class of Differential Equations with Delays [C] . Cheng Rong Fourth international conference on information and computing . 2011

机译：一类时滞微分方程的Maslov型指数和周期解的计算
5. PERIODIC SOLUTIONS OF A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS (THE VAN-DER-POL EQUATION). [D] . ECKWEILER, HOWARD JESSE. 1943

机译：一类非线性微分方程的周期解（范德波尔方程）。
6. Analytical Approximate Solutions for a General Class of Nonlinear Delay Differential Equations [O] . Bogdan Căruntu, Constantin Bota -1

机译：一般一类非线性时滞微分方程的解析近似解
7. Multiplicity results of periodic solutions for a class of first order delay differential equations [O] . Wu Ke, Wu Xian 2012

机译：一类一阶时滞微分方程周期解的多重性结果

MULTIPLICITY RESULTS FOR PERIODIC SOLUTIONS TO A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS

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