Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2010; 47(6): 1235-1250

Printed November 1, 2010

https://doi.org/10.4134/BKMS.2010.47.6.1235

Copyright © The Korean Mathematical Society.

Three solutions to a class of Neumann doubly eigenvalue elliptic systems driven by a $(p_{1},\ldots,p_{n})$-Laplacian

Ghasem A. Afrouzi, Shapour Heidarkhani, and Donal O'Regan

University of Mazandaran, Razi University, National University of Ireland

Abstract

In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a $(p_{1},\ldots,p_{n})$-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.

Keywords: three solutions, critical point, $(p_{1},\ldots,p_{n})$-Laplacian, multiplicity results, Neumann problem

MSC numbers: 35J65, 34A15