奇异三阶三点边值问题解的存在性

摘要

An existence theorem of solution is established for the nonlinear third-order three-point boundary value problem u"'(t)=f(t,u(t),u'(t),u"(t)) a.e.t∈[0,1], u(0)=a, u'(η)=b, u"(1)=c, where 1/2≤η<1. In this problem, the nonlinear term f(t,u,v,w) is a Caratheodory function and the boundary condition is nonhomogeneous. Main results are expressed by integral form.%对于非线性三阶三点边值问题:u"'(t)=f(t,u(t),u'(t),u"(t)) a.e.t∈[0,1],u(0)=a,u'(η)=b,u"(1)=c,建立了一个解的存在定理,其中1/2≤η<1.在这个方程中,非线性项f(t,u,v,w)是一个Caratheodoly函数并且边界条件是非齐次的.主要结论是用积分表达的.