高阶微分方程边值问题3个正解的存在性

On Existence of Multiple Solutions for Boundary Value Problem of Higher Differential Equation

主要讨论了一类高阶两点边值问题,首先利用已知的高阶两点边值问题的格林函数得到相关性质的结果,其次再利用 Leggett-Williams 不动点定理,详细研究以下高阶两点边值问题{-u (n)(t)=a(t)f(u(t)) t∈(0, 1)u (p)(1)=0, u (i)(0)=0 i=0,1,…,n-2 3个正解的存在性,其中n≥2, p∈{1, 2,…, n-2}.

A class of high order two-point boundary value problems has been discussed. Firstly using the green s function of the higher order two-point boundary value problem, the related properties have been obtained. Using the Leggett-Williams Fixed-Point Theorem, the existence of multiple solutions of following high order boundary value problem has been studied {u (n)(t)=a(t)f(u(t)) t∈(0, 1) u (p)(1)=0, u (i)(0)=0 i=0,1,…,n-2 where n≥2, p∈{1, 2,…, n-2}.