Electron. J. Differential Equations, Vol. 2022 (2022), No. 50, pp. 1-23.

Asymptotic behavior of cooperative systems involving p-Laplacian operators

Pablo Alvarez-Caudevilla

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.
DOI: https://doi.org/10.58997/ejde.2022.50

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Pablo Álvarez-Caudevilla
Departamento de Matemáticas
Universidad Carlos III de Madrid
Av. Universidad 30, 28911
Leganés, Madrid, Spain
email: pcaudev@math.uc3m.es

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