Solutions with prescribed mass for the p-Laplacian Schrödinger-Poisson system with critical growth

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F26%3A0198534" target="_blank" >RIV/00216305:26220/26:0198534 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022039625005972" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039625005972</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2025.113570" target="_blank" >10.1016/j.jde.2025.113570</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Solutions with prescribed mass for the p-Laplacian Schrödinger-Poisson system with critical growth

Popis výsledku v původním jazyce

In this paper, we focus on the existence and multiplicity of solutions for the p-Laplacian Schrödinger-Poisson system {−Δpu+γϕ|u|p−2u=λ|u|p−2u+μ|u|q−2u+|u|pu,inR3,−Δϕ=|u|p,inR3, with a prescribed mass given by ∫R3|u|pdx=ap, in the Sobolev critical case, where, 1<p<3,a>0, and γ>0, μ>0 are parameters, [Formula presented] is the Sobolev critical exponent, and λ∈R is an undetermined parameter, acting as a Lagrange multiplier. We investigate this system under the Lp-subcritical perturbation μ|u|q−2u, with [Formula presented], and establish the existence of multiple normalized solutions using the truncation technique, concentration-compactness principle, and genus theory. In the Lp-supercritical regime: [Formula presented], we prove two existence results for normalized solutions under different assumptions for the parameters γ,μ, by employing the Pohozaev manifold analysis, concentration-compactness principle and mountain pass theorem. This study presents new contributions regarding the existence and multiplicity of normalized solutions of the p-Laplacian critical Schrödinger-Poisson problem, perturbed with a subcritical term in the whole space R3, for the first time.

Název v anglickém jazyce

Solutions with prescribed mass for the p-Laplacian Schrödinger-Poisson system with critical growth

Popis výsledku anglicky

In this paper, we focus on the existence and multiplicity of solutions for the p-Laplacian Schrödinger-Poisson system {−Δpu+γϕ|u|p−2u=λ|u|p−2u+μ|u|q−2u+|u|pu,inR3,−Δϕ=|u|p,inR3, with a prescribed mass given by ∫R3|u|pdx=ap, in the Sobolev critical case, where, 1<p<3,a>0, and γ>0, μ>0 are parameters, [Formula presented] is the Sobolev critical exponent, and λ∈R is an undetermined parameter, acting as a Lagrange multiplier. We investigate this system under the Lp-subcritical perturbation μ|u|q−2u, with [Formula presented], and establish the existence of multiple normalized solutions using the truncation technique, concentration-compactness principle, and genus theory. In the Lp-supercritical regime: [Formula presented], we prove two existence results for normalized solutions under different assumptions for the parameters γ,μ, by employing the Pohozaev manifold analysis, concentration-compactness principle and mountain pass theorem. This study presents new contributions regarding the existence and multiplicity of normalized solutions of the p-Laplacian critical Schrödinger-Poisson problem, perturbed with a subcritical term in the whole space R3, for the first time.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

443

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

51

Strana od-do

1-51

Kód UT WoS článku

001523302100001

EID výsledku v databázi Scopus

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