摘要
研究了非线性四阶常微分方程u^((4))(t)=f(t,u(t),u'(t)),t∈[0,1]\E在边界条件u(0)=u'(0)=u''(1)=u'''(1)=0下的正解,其中E[0,1]是一个零测度的闭集,而非线性项f(t,u,v)可以在t∈E时奇异.通过构造适当的积分方程并利用锥上的不动点定理证明了这个方程在满足与n有关的条件下存在n个正解,其中n是某个自然数.
The positive solutions are studied for the nonlinear fourth-order ordinary differential equation u（4） （t） = f（t, u（t）, u＇（t））, t E [0, 1]／E, subject to the boundary conditions u（O） = u＇（O） = u″（1） = u″′（1） = O, where E C [0,1] is a closed set with measure zero and nonlinear term f（t, u, v） may be singular for t ∈ E. With some conditions, by constructing suitable integral equation and applying fixed point theorems on cone, the existence of n positive solutions is proved for the equations, where n is a positive integral number.
出处
《系统科学与数学》
CSCD
北大核心
2009年第1期63-69,共7页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(10571085)资助课题
关键词
非线性常微分方程
边值问题
正解
Nonlinear ordinary differential equation, boundary value problem, positive solution.
