Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2012; 49(1): 1-10

Printed January 1, 2012

https://doi.org/10.4134/BKMS.2012.49.1.1

Copyright © The Korean Mathematical Society.

Solvability for a class of the systems of the nonlinear elliptic equations

Tacksun Jung and Q-Heung Choi

Kunsan National University, Inha University

Abstract

Let $\Omega$ be a bounded subset of $\mathbb R^n$ with smooth boundary. We investigate the solvability for a class of the system of the nonlinear elliptic equations with Dirichlet boundary condition. Using the mountain pass theorem we prove that the system has at least one nontrivial solution.

Keywords: system of nonlinear elliptic equations, mountain pass theorem, $(P.S.)$ condition, critical point theory

MSC numbers: 35J50, 35J55, 35J20, 35Q72