The asymptotic behavior of solutions for a perturbed system of eigenvalue problems

In this article we study the existence of solutions for a family of perturbed eigenvalue problems described by a system consisting of two partial differential equations in which the differential operators involved are the sum between a p -Laplacian and a q -Laplacian with q≠ p q ≠ p but depending on p . Next, we study the asymptotic behavior, as p→ ∞ p → ∞ , of the sequence of solutions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions.