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- Title
A Note on the Existence Results for Schrödinger–Maxwell System with Super-Critical Nonlinearitie.
- Authors
Bahrouni, Anouar
- Abstract
The paper considers the following Schrödinger–Maxwell system with supercritical nonlinearitie, 0.1 { − Δ u + K (x) ϕ u = | u | p − 1 u + h (x) , in Ω , − Δ ϕ = K (x) u 2 , in Ω , ϕ = u = 0 , in ∂ Ω , where Ω ⊂ R 3 is a bounded domain with smooth boundary, 1 < p and K , h ∈ L ∞ (Ω) . We prove the existence of at least one non-trivial weak solution. This result is already known for the subcritical case. In this paper, we extend it to the supercritical values of p as well. We use a new variational principle to prove our result.
- Subjects
VARIATIONAL principles
- Publication
Acta Applicandae Mathematicae, 2020, Vol 166, Issue 1, p215
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-019-00263-3