一类完全非线性四阶微分方程正周期解的存在性  

Existence of Positive Periodic Solutions for a Class of Fully Fourth-order Nonlinear Differential Equations

作　　者：王晓萍 韩晓玲 WANG Xiaoping;HAN Xiaoling(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu)

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：《四川师范大学学报（自然科学版）》2024年第1期55-59,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11561063)。

摘　　要：讨论一类完全非线性四阶微分方程u^((4))(t)+a(t)u(t)=f(t,u(t),u′(t),u″(t),u″′(t))正周期解的存在性,其中,a(t)∈C([0,ω],(0,+∞)),f∈C([0,ω]×[0,+∞)×R^(3),[0,+∞)).在允许非线性项满足超线性增长不等式条件的情况下,利用Green函数和锥上的不动点理论,获得上述四阶微分方程正周期解的存在性结果,并通过例子验证了主要结果的有效性.In this paper,we consider the existence of positive periodic solutions for a class of fully fourthorder nonlinear differential equations u^((4))(t)+a(t)u(t)=f(t,u(t),u′(t),u″(t),u″′(t)),where a(t)∈C([0,ω],(0,+∞))and f∈C([0,ω]×[0,+∞)×R^(3),[0,+∞)).When the nonlinearity satisfies the condition of superlinear growth inequality,by using Green's function and fixed point theorem in cones,the existence for positive periodic solutions to the above fourthorder nonlinear differential equations is obtained.Moreover,one example is given to demonstrate the validity of our main results.

关 键 词：完全非线性四阶微分方程 正周期解 锥上的不动点理论 GREEN函数 

分 类 号：O175.14[理学—数学]