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一类二阶中立型泛函微分方程的无穷多个次调和周期解
Infinite Subharmonic Periodic Solutions to a Class of Second-order Neutral Differential Equations
【摘要】 本文通过变分原理和Z2不变群指标,得出了下述二阶中立型泛函微分方程存在无穷多个次调和周期解的充分条件(p(t)(μx′(t))+x′(t-τ)+μx′(t-2τ))′-q(t)x(t)+f(t,x(t),x(t-τ),x(t-2τ))=0,|μ|<1/2.
【Abstract】 In this paper,by critical point and Z2-group index theory,we obtain infinite subharmonic periodic solutions to second-order nonlinear non-autonomous Sturm-Liouville neutral functional differential equations(p(t)(μx’(t))+x’(t-τ)+μx’(t-2τ))’-q(t)x(t)+f(t,x(t),x(t-τ),x(t-2τ))=0,|μ|<1/2.
【关键词】 Z2不变群指标;
中立型泛函微分方程;
临界点;
周期解;
【Key words】 Z2-group index theory; Neutral nonlinear functional differential equations; Critical points; Periodic solutions;
【Key words】 Z2-group index theory; Neutral nonlinear functional differential equations; Critical points; Periodic solutions;
【基金】 湖南省博士后基金(2006FJ4249);广东省自然科学基金(031608);国家自然科学基金(10471155)
- 【文献出处】 应用数学 ,Mathematica Applicata , 编辑部邮箱 ,2008年03期
- 【分类号】O174.3
- 【被引频次】6
- 【下载频次】66