Multiplicity results for discrete anisotropic equations

Marek Galewski; Shapour Heidarkhani; Amjad Salari

doi:10.3934/dcdsb.2018014

Article Contents

2018, Volume 23, Issue 1: 203-218. Doi: 10.3934/dcdsb.2018014

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Multiplicity results for discrete anisotropic equations

1.
Institute of Mathematics, Technical University of Lodz, Wolczanska 215, 90-924 Lodz, Poland
2.
Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran
3.
Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

* Corresponding authorr: Marek Galewski
* Corresponding authorr: Marek Galewski

Received: October 31, 2016

Published: November 2017

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Abstract

In this article we continue the study of discrete anisotropic equations and we will provide a new multiplicity results of the solutions for a discrete anisotropic equation. The procedure viewed here is according to variational methods and critical point theory. In fact, using a consequence of the local minimum theorem due Bonanno and mountain pass theorem we look into the existence results for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by mingling two algebraic conditions on the nonlinear term employing two consequences of the local minimum theorem due Bonanno we guarantee the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem.

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Mathematics Subject Classification: 34B15, 39A10, 39A70, 46E39.

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