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Critical quasilinear elliptic systems with convex subcritical perturbations
Abstract
We study a class of Dirichlet problems for coupled quasilinear elliptic systems driven by the p--Laplacian in a bounded domain, where the nonlinear terms split into a critical homogeneous part and a convex subcritical perturbation. Using variational methods, a nonlinear eigenvalue theory based on the Fadell--Rabinowitz ℤ2--cohomological index, and a refined linking construction, we prove the existence of a nontrivial solution for every parameter value under suitable dimensional assumptions. We also treat a nonhomogeneous version with small forcing terms by applying a recent abstract perturbation theorem, yielding the existence of two distinct nontrivial solutions.
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BibTeX
@misc{gloss2026critical,
title = {{Critical quasilinear elliptic systems with convex subcritical perturbations}},
author = {Elisandra Gloss and Bruno Ribeiro and Artur Jorge Marinho and Kanishka Perera},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28267},
eprint = {2609.28267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28267},
}
RIS
TY - UNPB
TI - Critical quasilinear elliptic systems with convex subcritical perturbations
AU - Elisandra Gloss
AU - Bruno Ribeiro
AU - Artur Jorge Marinho
AU - Kanishka Perera
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.28267
UR - https://arxiv.org/abs/2609.28267
AB - We study a class of Dirichlet problems for coupled quasilinear elliptic systems driven by the p--Laplacian in a bounded domain, where the nonlinear terms split into a critical homogeneous part and a convex subcritical perturbation. Using variational methods, a nonlinear eigenvalue theory based on the Fadell--Rabinowitz ℤ_2--cohomological index, and a refined linking construction, we prove the existence of a nontrivial solution for every parameter value under suitable dimensional assumptions. We also treat a nonhomogeneous version with small forcing terms by applying a recent abstract perturbation theorem, yielding the existence of two distinct nontrivial solutions.
ER -