摘要
讨论了含导数项的四阶常微分方程边值问题u(4)(t)=f(t,u,u′,u″), t∈[0,1],u(0)=u′(1)=u″(0)=u (1)=0解的存在性,其中f(t,u,v,w):[0,1]×R×R×RR为Carath啨odory函数.通过上下解方法获得了解的存在性结果.
The existence of solutions for the four th-order boundary valve problem with derivative term u-((4)_(t)=f(t,u,u′,u″), t∈[0,1], u(0)=u′(1)=u″(0)=u(1)=0 is discussed,where f:[ 0 ,1]× R×R×RR is a Carathéodory function. An existence theorem of solutions is established by using the method of upper and lower solution.
出处
《西北师范大学学报（自然科学版）》
CAS
2004年第3期4-7,共4页
Journal of Northwest Normal University(Natural Science)
关键词
四阶边值问题
弱极值原理
二阶积分微分方程
上下解方法
four th-or der boundary value problem
weak maximum principle
secon d-or der integ ro-di fferential equation
the method of lower and upper solution
