Existence of three solutions for a class of Dirichlet quasilinear elliptic systems involving the (p1, ..., pn)-Laplacian

被引：35

作者：

Afrouzi, G. A. ^{[1
]}

Heidarkhani, S. ^{[1
]}

机构：

[1] Univ Mazandaran, Fac Basic Sci, Dept Math, Babol Sar, Iran

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 01期

关键词：

Three solutions; Critical point; (p(1); .; p(n))-Laplacian; Multiplicity results; Dirichlet problem; 2 NONTRIVIAL SOLUTIONS;

D O I：

10.1016/j.na.2007.11.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the existence of at least three weak solutions for the quasilinear elliptic systems {Delta(p1)u(1) + lambda F-u1(x, u(1), u(2), ..., u(n)) = 0 in Omega, Delta(p2)u(2) + lambda F-u2(x, u(1), u(2), ..., u(n)) = 0 in Omega, ... D(pn)u(n) + lambda F-un(x, u(1), u(2), ..., u(n)) = 0 in Omega, u(i) = 0 for 1 <= i <= n on partial derivative Omega. Our main tool is a recent three critical points theorem of Ricceri [B. Ricceri, On a three critical points theorem, Arch. Math. (Base]) 75 (2000) 220-226]. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：135 / 143

页数：9

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