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PERTURBATION EFFECTS FOR THE MINIMAL SURFACE EQUATION WITH MULTIPLE VARIABLE EXPONENTS
Journal article   Peer reviewed

PERTURBATION EFFECTS FOR THE MINIMAL SURFACE EQUATION WITH MULTIPLE VARIABLE EXPONENTS

Ramzi Alsaedi and Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Discrete and continuous dynamical systems. Series S, Vol.12(2), pp.139-150
01/04/2019
DOI: https://doi.org/10.3934/dcdss.2019010

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We are concerned with the existence of nontrivial weak solutions for a class of generalized minimal surface equations with subcritical growth and Dirichlet boundary condition. In relationship with the values of several variable exponents, we establish two sufficient conditions for the existence of solutions. In the first part of this paper, we prove the existence of a nonnegative solution. Next, we are concerned with the existence of infinitely many solutions in a symmetric abstract setting.

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