二阶微分方程组正周期解的存在性  

Existence of positive periodic solutions for second order differential equations

作　　者：陈伟[1] 

机构地区：[1]河海大学理学院,南京210098

出　　处：《黑龙江大学自然科学学报》2013年第3期290-295,共6页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11171090)

摘　　要：考虑二阶微分方程组{x″+H(t)x'+A(t)x=F(t,x),0<t<T,x(0)=x(T),x'(0)=x'(T{),正周期解的存在性。利用Krasnoselskii不动点定理以及所对应的格林函数正性,证明上述二阶微分方程组新的正周期解的存在定理,将所得结论进行推广,得到上述二阶微分方程组多个正周期解的存在定理。将结论应用在经典实例上,验证了所得结果的正确性。The existence of positive periodic solutions for the following second order differential equations is considered.{x＂＋H（t）x＇＋A（t）x=F（t,x）,0〈t〈T,x（0）=x（T）,x＇（0）=x＇（T）. First of all, by using the Krasnoselskii fixed point theorem and the positivity of the Green＇ s function, the new existence theorem of positive periodic solutions of the equations is obtained ; Then, the above main conclusions are generalized to existence theorem of multiple positive periodic solutions ; Finally, a classic example is tested to present the value of the main results.

关 键 词：正周期解 二阶微分方程组 格林函数 KRASNOSELSKII不动点定理 

分 类 号：O175[理学—数学]