一类非自治四阶常微分方程正周期解的存在性  

Existence of positive periodic solutions for a class of non-autonomous fourth-order ordinary differential equations

作　　者：杨虎军 韩晓玲 YANG Hu-jun;HAN Xiao-ling(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2020年第6期109-114,121,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11561063);西北师范大学研究生科研资助项目(2019KYZZ012035)。

摘　　要：研究一类非自治四阶常微分方程u^(iv)+pu″+a(x)u^n-b(x)u n+1-c(x)u^n+2=0周期解的存在性,其中p≥-1,n为有限正整数,a(x)、b(x)、c(x)是连续的T-周期函数。运用Mawhin延拓定理,证明这一类方程正周期解的存在性。This paper studies the existence of positive periodic solutions for a class of non-autonomous fourth-order ordinary differen-tial equations u^(iv)+pu″+a(x)u^n-b(x)u^n+1-c(x)u^n+2=0,where p≥-1,n is a finite positive integer,a(x),b(x),c(x)are continuous T-periodic functions.By using Mawhin's continuation theorem,the existence of positive periodic solutions for this kind of equations is proved.

关 键 词：四阶常微分方程 Mawhin延拓定理 存在性 非自治 正周期解 

分 类 号：O175.14[理学—数学]