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 {equation presented} 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 {equation presented}, in various functional settings which are suitable for both variational and perturbation methods.

On a class of nonlinear Schrödinger-Poisson systems involving a nonradial charge density / Mercuri, C.; Tyler, T. M.. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 36:4(2020), pp. 1021-1070. [10.4171/RMI/1158]

On a class of nonlinear Schrödinger-Poisson systems involving a nonradial charge density

Mercuri C.;
2020-01-01

Abstract

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 {equation presented} 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 {equation presented}, in various functional settings which are suitable for both variational and perturbation methods.
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On a class of nonlinear Schrödinger-Poisson systems involving a nonradial charge density / Mercuri, C.; Tyler, T. M.. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 36:4(2020), pp. 1021-1070. [10.4171/RMI/1158]
Mercuri, C.; Tyler, T. M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1292208
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