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
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.File | Dimensione | Formato | |
---|---|---|---|
MercuriTyleracceptedversion.pdf
Open access
Tipologia:
Versione dell'autore revisionata e accettata per la pubblicazione
Dimensione
525.04 kB
Formato
Adobe PDF
|
525.04 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris