# American Institute of Mathematical Sciences

April  2019, 12(2): 139-150. doi: 10.3934/dcdss.2019010

## Perturbation effects for the minimal surface equation with multiple variable exponents

 Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

* Corresponding author

This paper is dedicated to Prof. Vicenţiu Rǎdulescu on the occasion of his 60th anniversary

Received  May 2017 Revised  November 2017 Published  August 2018

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 non-negative solution. Next, we are concerned with the existence of infinitely many solutions in a symmetric abstract setting.

Citation: Ramzi Alsaedi. Perturbation effects for the minimal surface equation with multiple variable exponents. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 139-150. doi: 10.3934/dcdss.2019010
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##### References:
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