In this paper we are going to prove existence and regularity results for positive solutions of the following elliptic system: −div(M(x)∇u)+rφur−1=f+φr,−div(M(x)∇φ)+ruφr−1=ur.where Ω is a bounded open subset of RN, M is a bounded, uniformly elliptic matrix, r>1, and f≥0 belongs to some Lebesgue space Lm(Ω), with m≥1. We will also prove the relationships of the solutions of the system with saddle points of the integral functional [Formula presented]
A semilinear system of Schrödinger–Maxwell equations / Boccardo, L.; Orsina, L.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 194:(2020). [10.1016/j.na.2019.02.007]
A semilinear system of Schrödinger–Maxwell equations
Boccardo L.;Orsina L.
2020
Abstract
In this paper we are going to prove existence and regularity results for positive solutions of the following elliptic system: −div(M(x)∇u)+rφur−1=f+φr,−div(M(x)∇φ)+ruφr−1=ur.where Ω is a bounded open subset of RN, M is a bounded, uniformly elliptic matrix, r>1, and f≥0 belongs to some Lebesgue space Lm(Ω), with m≥1. We will also prove the relationships of the solutions of the system with saddle points of the integral functional [Formula presented]File allegati a questo prodotto
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