Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 50, pp. 1-23.

Title: Asymptotic behavior of cooperative systems involving p-Laplacian operators
       
Author: Pablo Alvarez-Caudevilla (Univ. Carlos III, Madrid, Spain)

Abstract:  
This work is devoted to the analysis of the asymptotic behavior of a parameter
dependent quasilinear cooperative eigenvalue system when a parameter in front of some
non-negative potentials approaches infinity.
In particular we consider operators of p-Laplacian type.
We prove that the eigenfunctions concentrate on the subdomains
where those potentials vanish at the limit, while the eigenvalue approaches
an upper bound that will depend on those subdomains.
We also show several properties for the unusual limiting problems.

Submitted December 22, 2021. Published July 15, 2022.
Math Subject Classifications: 35J47, 35P20, 49R05.
Key Words: Cooperative systems; p-Laplacian; eigenvalue problems.