On a class of nonlinear Schrödinger–Poisson systems involving a nonradial charge density
- Autores: Carlo Mercuri, Teresa Megan Tyler
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 4, 2020, págs. 1021-1070
- Idioma: inglés
- DOI: 10.4171/rmi/1158
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Resumen
In the spirit of the classical work of P. H. Rabinowitz on nonlinear Schrödinger equations, we prove existence of mountain-pass solutions and least energy solutions to the nonlinear Schrödinger–Poisson system {−Δu+u+ρ(x)ϕu=|u|p−1u,−Δϕ=ρ(x)u2,x∈R3,x∈R3, under different assumptions on ρ:R3→R+ at infinity. Our results cover the range p∈(2,3) where the lack of compactness phenomena may be due to the combined effect of the invariance by translations of a 'limiting problem' at infinity and of the possible unboundedness of the Palais–Smale sequences. Moreover, we find necessary conditions for concentration at points to occur for solutions to the singularly perturbed problem
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