一类非线性边值问题的三重正解

研究边值问题:-y~(6)(t)=f(y(t),-y~n(t),y~(4)(t)) 0≤t≤1 y(0)=y′(1)=0 y~n(0)=y~n(1)=0 y~(4)(0)=y~(4)(1)=0其中f≥0,其边值条件不同于Lidstone边值条件,应用Leggett-williams不动点定理和格林函数得到边值问题存在三重正解的充分条件.

Triple Positive Solutions of a Kind of Nonlinear Boundary Value Problem

In this paper, the authors consider the nonlinear boundary value problem (BVP):{-y(6)(t) = f(y(t), -y"(t), y(4)(t)) t ∈ [0, 1]y(0) = y'(1) = 0y"(0) = y"(1) = 0y(4)(0) = y(4)(1) = 0}where, f＞0. The boundary conditions are different from the Lidstone boundary conditions. By using the Leggett-Williams Fixed Point Theroem and inequalities involving an associated green's function, a sufficient condition for the existence of triple positive concave solutions of BVP is obtained.