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

Abstract

In this article, we deal with 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.

Keywords

• $p(x)$-laplacian
• variable exponents
• weak solution
• eigenvalue
• regularity
• boundedness