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Anisotropic quasilinear elliptic systems involving nonlinearities with negative critical terms
Abstract
In this paper we investigate existence and multiplicity of solutions for a critical growth anisotropic quasilinear elliptic system, depending on two real parameters λ, μ, that is coupled through a subcritical perturbation term and involves a negative critical part. We identify a specific scaling for the system and introduce a parameter γ associated with this scaling, which governs the geometry of the corresponding variational functional. We establish three distinct types of multiplicity results, depending on the regimes γ= 1, γ> 1, and γ< 1. The multiple results of multiplicity of solutions are based on a recent abstract critical point theorem for symmetric functionals on product spaces when γ≥1 and on a truncation argument for γ<1.
Related
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BibTeX
@misc{gloss2026anisotropic,
title = {{Anisotropic quasilinear elliptic systems involving nonlinearities with negative critical terms}},
author = {Elisandra Gloss and Artur Jorge Marinho and Kanishka Perera},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32629},
eprint = {2609.32629},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32629},
}
RIS
TY - UNPB
TI - Anisotropic quasilinear elliptic systems involving nonlinearities with negative critical terms
AU - Elisandra Gloss
AU - Artur Jorge Marinho
AU - Kanishka Perera
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32629
UR - https://arxiv.org/abs/2609.32629
AB - In this paper we investigate existence and multiplicity of solutions for a critical growth anisotropic quasilinear elliptic system, depending on two real parameters λ, μ, that is coupled through a subcritical perturbation term and involves a negative critical part. We identify a specific scaling for the system and introduce a parameter γ associated with this scaling, which governs the geometry of the corresponding variational functional. We establish three distinct types of multiplicity results, depending on the regimes γ= 1, γ> 1, and γ< 1. The multiple results of multiplicity of solutions are based on a recent abstract critical point theorem for symmetric functionals on product spaces when γ≥1 and on a truncation argument for γ<1.
ER -