带阻尼项的二阶奇异微分方程的正周期解  

Positive periodic solutions for second-order singular differential equations with damping terms

作　　者：陈瑞鹏 李小亚 CHEN Rui-peng;LI Xiao-ya(College of Mathematics and Information Science, North Minzu University, Yinchuan 750021, Ningxia, China)

机构地区：[1]北方民族大学数学与信息科学学院

出　　处：《山东大学学报（理学版）》2019年第8期33-41,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11701012);北方民族大学重大专项资助项目(ZDZX201804);宁夏高等教育一流学科建设资助项目(NXYLXK2017B09)

摘　　要：研究带阻尼项的二阶微分方程u″+p(t)u′+q(t)u=f(t,u)+c(t)正周期解的存在性,其中p,q,c∈L^1(R/TZ;R),f为Carathéodory函数且在u=0处具有奇异性。运用不动点理论,为该方程建立了若干正周期解的存在性结果,所得结果推广并改进了已有文献的相关结论。This paper studies the existence of positive periodic solutions of u″+p(t)u′+q(t)u=f(t,u)+c(t), where p,q,c∈L^1(R/TZ;R), f is a Carathéodory function and is singular when u=0. By means of the fixed point theory, several existence theorems are established for the above equation, and some recent results in the literature are generalized and improved.

关 键 词：正周期解 存在性 奇性 不动点理论 

分 类 号：O175.8[理学—数学]