一类四阶周期边值问题解的存在性与唯一性  

Existence and uniqueness of solutions for a class fourth-order periodic boundary value problems

作　　者：王天祥 李永祥 WANG Tian-xiang;LI Yong-xiang(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7期16-21,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11661071)。

摘　　要：运用Leray-Schauder不动点定理,讨论四阶周期边值问题{u^(4)(t)=f(t,u(t),u'(t)),t∈[0,1],u^(i)(0)=u^(i)(1),i=0,1,2,3解的存在性与唯一性,其中f:[0,1]×R^2→R连续。在允许非线性项f(t,x,y)关于x、y超线性增长的不等式条件下,获得了该问题解的存在性与唯一性。By using Leray-Schauder fixed point theorem,this paper discusses the existence and uniqueness of solutions for the fourth-order periodic boundary value problem{u^(4)(t)=f(t,u(t),u'(t)),t∈[0,1],u^(i)(0)=u^(i)(1),i=0,1,2,3,where f:[0,1]×R^2→R continuous.existence and uniqueness of solutions is obtained under the inequality conditions that allow the nonlinear term f(t,x,y)to grow superlinearly on x and y.

关 键 词：四阶周期边值问题 存在性与唯一性 超线性增长 LERAY-SCHAUDER不动点定理 

分 类 号：O75.8[理学—晶体学] O177.91