奇异多点边值问题的多个正解

Multiple Positive Solutions to Singular(k,n-k) Multi-Point Boundary Value Problems

利用非线性泛函分析中半序Banach空间的锥理论和不动点指数方法,在两种多点边值条件下,当右端非线性函数f满足一定增长性条件时,证明了右端分离变量型奇异高阶(k,n-k)多点边值问题存在多个正解的结论,其中允许h(x)在边界点处奇异.最后将本文的结论应用到一个具体的奇异三阶三点边值问题,得到了存在三个正解的结果.

Making use of cone theory and fixed point index method in partial order Banach space in nonlinear functional analysis,we prove the existence of multiple positive solutions to the singular higher order （k, n - k ） multi-point boundary value problems with the right-hand h （x）f（ u ） of separating variable type if there are two multi-point boundary values and the right- hand nonlinear function f satisfies certain conditions of growth, in which h （x） is allowed to be singular at boundary points. This conclusion is applied to a concrete singular third-order three-point boundary value problem to which there are three positive solutions.