On the first eigenvalue for a (p(x),q(x))-Laplacian elliptic system
  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. 
Abdelkrim Moussaoui, Jean V\'elin
math.AP