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A p-Laplacian Schrödinger--Maxwell system with rapidly growing nonlinearities
Abstract
Let Ω⊂RN, N≥2, be a bounded domain and let 1<p<∞. Inspired by the exponential case treated in \cite{BO2026}, we study the quasilinear Schrödinger--Maxwell system −Δp u+ψG'(u)=f &in Ω, −Δpψ=G(u) &in Ω, u=ψ=0 &on ∂Ω, where G∈ C1(R) is even, convex, nonnegative and nontrivial, with G(0)=0, and satisfies G(t)≲ 1+|G'(t)| for large |t|. Under the assumption |f|ln(1+|f|)∈ L1(Ω), we prove the existence of a finite-energy weak solution and show that the solution is a saddle point of the associated functional.
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BibTeX
@misc{silva2026plaplacian,
title = {{A $p$-Laplacian Schrödinger--Maxwell system with rapidly growing nonlinearities}},
author = {Genival da Silva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10878},
eprint = {2609.10878},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10878},
}
RIS
TY - UNPB
TI - A p-Laplacian Schrödinger--Maxwell system with rapidly growing nonlinearities
AU - Genival da Silva
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10878
UR - https://arxiv.org/abs/2609.10878
AB - Let Ω⊂R^N, N≥2, be a bounded domain and let 1<p<∞. Inspired by the exponential case treated in \cite{BO2026}, we study the quasilinear Schrödinger--Maxwell system −Δ_p u+ψG'(u)=f &in Ω, −Δ_pψ=G(u) &in Ω, u=ψ=0 &on ∂Ω, where G∈ C^1(R) is even, convex, nonnegative and nontrivial, with G(0)=0, and satisfies G(t)≲ 1+|G'(t)| for large |t|. Under the assumption |f|ln(1+|f|)∈ L^1(Ω), we prove the existence of a finite-energy weak solution and show that the solution is a saddle point of the associated functional.
ER -