Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU151494" target="_blank" >RIV/00216305:26220/24:PU151494 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00209-024-03520-w" target="_blank" >https://link.springer.com/article/10.1007/s00209-024-03520-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00209-024-03520-w" target="_blank" >10.1007/s00209-024-03520-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration

Popis výsledku v původním jazyce

In this paper, we are concerned with the study of the following 2-D Schrödinger–Poisson equation with critical exponential growth −ε^2delta u + V (x)u + ε−α (Iα ∗ |u|q )|u|q−2u = f (u), where ε > 0 is a parameter, Iα is the Riesz potential, 0 < α < 2, V ∈ C(R2, R), and f ∈ C(R, R) satisfies the critical exponential growth. By variational methods, we first prove the existence of ground state solutions for the above system with the periodic potential. Then we obtain that there exists a positive ground state solution of the above system concentrating at a global minimum of V in the semi-classical limit under some suitable conditions. Meanwhile, the exponential decay of this ground state solution is detected. Finally, we establish the multiplicity of positive solutions by using the Ljusternik–Schnirelmann theory.

Název v anglickém jazyce

Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration

Popis výsledku anglicky

In this paper, we are concerned with the study of the following 2-D Schrödinger–Poisson equation with critical exponential growth −ε^2delta u + V (x)u + ε−α (Iα ∗ |u|q )|u|q−2u = f (u), where ε > 0 is a parameter, Iα is the Riesz potential, 0 < α < 2, V ∈ C(R2, R), and f ∈ C(R, R) satisfies the critical exponential growth. By variational methods, we first prove the existence of ground state solutions for the above system with the periodic potential. Then we obtain that there exists a positive ground state solution of the above system concentrating at a global minimum of V in the semi-classical limit under some suitable conditions. Meanwhile, the exponential decay of this ground state solution is detected. Finally, we establish the multiplicity of positive solutions by using the Ljusternik–Schnirelmann theory.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

MATHEMATISCHE ZEITSCHRIFT

ISSN

0025-5874

e-ISSN

1432-8232

Svazek periodika

307

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

25

Strana od-do

1-25

Kód UT WoS článku

001238245700005

EID výsledku v databázi Scopus

2-s2.0-85195398625