一类四阶周期边值问题解的存在性与唯一性

doi:10.6040/j.issn.1671-9352.0.2019.788

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (7): 16-21.doi: 10.6040/j.issn.1671-9352.0.2019.788

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一类四阶周期边值问题解的存在性与唯一性

王天祥,李永祥^*

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2020-07-08
作者简介:王天祥(1992— ),男,硕士研究生,研究方向为非线性泛函分析. E-mail:wangtx1453071783@163.com*通信作者简介:李永祥(1963— ),男,博士,教授,博士生导师,研究方向为非线性泛函分析. E-mail:liyx@nwnu.edu.cn
基金资助:
国家自然科学基金资助项目(11661071)

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

WANG Tian-xiang, LI Yong-xiang^*

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2020-07-08

摘要/Abstract

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］×R²→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。

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

Abstract: 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］×R²→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.

Key words: fourth-order periodic boundary value problem, existence and uniqueness, superlinear growth, Leray-Schauder fixed point theorem

中图分类号:

O175.8

王天祥,李永祥. 一类四阶周期边值问题解的存在性与唯一性[J]. 《山东大学学报(理学版)》, 2020, 55(7): 16-21.

WANG Tian-xiang, LI Yong-xiang. Existence and uniqueness of solutions for a class fourth-order periodic boundary value problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(7): 16-21.

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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

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