一类带p-Laplace型算子的高阶两点边值问题的极值解  

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

作　　者：苗利军[1,2] 裴明鹤[1] 

机构地区：[1]北华大学数学学院,吉林132013 [2]白城师范学院数学学院,白城137000

出　　处：《应用数学学报》2012年第2期356-374,共19页Acta Mathematicae Applicatae Sinica

摘　　要：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)=A_i,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-Caratheodory函数,A,B,A_i,B_i∈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.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 L^1-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.

关 键 词：边值问题 p-Laplace型算子 单调迭代方法 极值解 

分 类 号：O175.8[理学—数学]