p-Laplacian方程边界问题的多解性(英文)  

Multiplicity Solutions for the Dirichlet Problem Involving the p-Laplacian

作　　者：徐高[1] 刘振海[1] 

机构地区：[1]长沙理工大学,长沙410077

出　　处：《数学理论与应用》2011年第2期64-68,共5页Mathematical Theory and Applications

摘　　要：在这一篇文章中我们讨论下面这个方程:-Δpu=λf(x,u)inΩ u=0 on Ω,其中Ω是具有光滑边界的有界开集,Ω,p>n,λ>0,且f:Ω×R→R是一个Caratheodory泛函,满足下列条件,存在t>0,使得supt∈[0,t]︱f(.,t)︱∈L∞(Ω),我们可以得出上面方程存在至少三个解。In this paper we present a result of existence of multiplicity solutions to the following Dirichlet problem involving the p- Laplacian：{-△ρu=λf（x,u）in Ω,where Ω∈R^N is a bounded open set with sufficiently smooth bounded ЭΩ,p〉n,λ〉0,and f：Ω×R→R is a Caratheodory function satisfying the following condition ： There exists t〉0 such that sup_｜f（·t）｜∈L^＊（Ω）.Precisely, our result ensure the existence of at least three weak solutions to the above problem.

关 键 词：能量泛函 临界点 嵌入定理 三临界点定理 

分 类 号：O175.8[理学—数学]