一类带p-Laplace型算子的高阶两点边值问题的极值解

本文主要研究一类带p-Laplace型算子的n(≥3)阶非线性常微分方程-φ(u(n-1)(t))]'=f(t,u(t)), a.e.t∈a,b]满足两点边界条件u(i)(a)=Ai, i＝0,1,…,n-3, u(n-1)(a)=A, u(n-1)(b)=B的边值问题极值解的存在性,这里φ:R→R=(-∞,+∞)是递增的同胚,f:a,b]×R→R是L 1-Carathéodory函数,A,B,Ai,Bi∈R,i=0,1,…,n-3.主要利用基于反极大值原理的单调迭代方法,得到了上述边值问题极值解的存在性结果.

Extremal Solutions for a Higher Order Two Point Boundary Value Problem with p-Laplacian-like Operator

In this paper,we will consider the existence of extremal solutions for a nth-order differential equation withρ-Laplacian-like operator -φ(u^（n-1）（t）)]’=f（t,u（t））,a.e.t∈a,b] subject to the following two-point boundary conditions u^（i）（a）=A_i,i=0,1,…,n-3,u^（n-1）（a）=A,u^（n-1）（b）=B, whereφ:（?）→（?）=（-∞,+∞） is an increasing homeomorphism,f:a,b]×（?）→（?） is L¹-Caratheodory function,and A,B,A_i,B_i∈（?）,i = 0,1,? ? ?,n-3.The existence result of extremal solutions for the problem is obtained via monotone iterative techniques which are based on anti-maximum principles.