摘要
考察了三阶非线性常微分方程边值问题{u'''(t)=f(t,u(t),u'(t),u''(t)),a.e.0<t<1,u(0)=u'(0)=u'(1)=0,其中f:[0,1]×R3→R满足Carathéodory条件。在非线性项f满足适当增长性条件下,三阶非线性常微分方程边值问题至少存在1个解。基于Leray-Schauder不动点定理证明了主要结果。
In this paper,we consider the boundary value problems of third-order nonlinear ordinary differential equation{u'''(t)=f(t,u(t),u'(t),u''(t)),a.e.0<t<1,u(0)=u'(0)=u'(1)=0,where f:[0,1]×R3→R satisfies Carathéodory conditions.Under some suitable growth conditions on f,we show that the above problem has at least one solution.The proof of the main results is based on Leray-Schauder fixed point theorem.
作者
王丽媛
马如云
WANG Liyuan;MA Ruyun(School of Mathematics and Statistics,Xidian University,Xi'an 710126,Shaanxi Province,China)
出处
《浙江大学学报(理学版)》
CAS
CSCD
北大核心
2024年第3期273-276,共4页
Journal of Zhejiang University(Science Edition)
基金
国家自然科学基金资助项目(12061064).