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.
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页码：135 / 143
页数：9
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