We prove the existence of ground state solutions for the nonlinear
Schrodinger-Maxwell equations.Comment: 27 page

A. Azzollini

A. Pomponio

Azzollini

Benci

Berestycki

Brezis

Candela

Cassani

Cingolani

Coclite

Coleman

D'Aprile

d'Avenia

Kikuchi

Lazzo

Lions

Pisani

Rabinowitz

Ruiz

Salvatore

Talenti

Wang

Willem

English

arXiv

In this paper we study the nonlinear Schrödinger–Maxwell equations

−\Delta u + V (x)u +φu = |u|^{p−1}u in R3,
−\Delta φ = u^2 in R^3.
If V is a positive constant, we prove the existence of a ground state solution (u,φ) for 2 <
p < 5. The non-constant potential case is treated for 3 < p < 5, and V possibly unbounded
below. Existence and nonexistence results are proved also when the nonlinearity exhibits
a critical growth

AZZOLLINI, ANTONIO

A. POMPONIO

Archivio della Ricerca - Università della Basilicata

Ground state solutions for the nonlinear Schrodinger-Maxwell equations

Crossref

Ground state solutions for the nonlinear Schrödinger–Maxwell equations

AbstractIn this paper we study the nonlinear Schrödinger–Maxwell equations{−Δu+V(x)u+ϕu=|u|p−1uin R3,−Δϕ=u2in R3. If V is a positive constant, we prove the existence of a ground state solution (u,ϕ) for 2<p<5. The non-constant potential case is treated for 3<p<5, and V possibly unbounded below. Existence and nonexistence results are proved also when the nonlinearity exhibits a critical growth

Ground state solutions to the nonlinear Schrodinger-Maxwell equations

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Archivio della Ricerca - Università della Basilicata

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