On the first eigenvalue for a (p(x),q(x))-Laplacian elliptic system

TL;DR

This paper investigates the first eigenvalue of a nonlinear elliptic system with variable exponent growth, establishing key properties of eigenfunctions such as positivity, boundedness, and regularity.

Contribution

It introduces new results on the first eigenvalue and eigenfunctions for a (p(x),q(x))-Laplacian system with variable exponents, including positivity and regularity properties.

Findings

Eigenfunctions are positive and bounded.

Eigenfunctions exhibit regularity.

First eigenvalue characterized for the system.

Abstract

In this article, we deal about the first eigenvalue for a nonlinear gradient type elliptic system involving variable exponents growth conditions. Positivity, boundedness and regularity of associated eigenfunctions for auxiliaries systems are established.