The asymptotic behavior of solutions for a perturbed system of eigenvalue problems
Abstract
Abstract 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 $$q\ne p$$ q ≠ p but depending on p . Next, we study the asymptotic behavior, as $$p\rightarrow \infty $$ 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.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Journal of Elliptic and Parabolic Equations
- Volume
- 12
- Issue
- 1
- Pages
- 1147–1171
- Publication date
- 12 March 2026
- Language
- EN