Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU151078" target="_blank" >RIV/00216305:26220/24:PU151078 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00209-024-03432-9" target="_blank" >https://link.springer.com/article/10.1007/s00209-024-03432-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00209-024-03432-9" target="_blank" >10.1007/s00209-024-03432-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth

Popis výsledku v původním jazyce

The paper deals with the existence of normalized solutions for the following Schr & ouml;dinger-Poisson system with -constraint: { -Delta u+lambda u+mu(log||& lowast;u2)u=(e(u2-)1-u2)u,x is an element of R-2, integral R(2)u(2)dx=c, where mu>0,lambda is an element of R , will arise as a Lagrange multiplier and the nonlinearity enjoys critical exponential growth of Trudinger-Moser type. By specifying explicit conditions on the energy level c, we detect a geometry of local minimum and a minimax structure for the corresponding energy functional, and prove the existence of two solutions, one being a local minimizer and one of mountain-pass type. In particular, to catch a second solution of mountain-pass type, some sharp estimates of energy levels are proposed, suggesting a new threshold of compactness in the -constraint. Our study extends and complements the results of Cingolani-Jeanjean (SIAM J Math Anal 51(4): 3533-3568, 2019) dealing with the power nonlinearity a|u|p-2uin the case ofa>0andp>4, in the case of and , which seems to be the first contribution in the context of normalized solutions. Our model presents some new difficulties due to the intricate interplay between a logarithmic convolution potential and a nonlinear term of critical exponential type and requires a novel analysis and the implementation of new ideas, especially in the compactness argument. We believe that our approach will open the door to the study of other -constrained problems with critical exponential growth, and the new underlying ideas are of future development and applicability.

Název v anglickém jazyce

Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth

Popis výsledku anglicky

The paper deals with the existence of normalized solutions for the following Schr & ouml;dinger-Poisson system with -constraint: { -Delta u+lambda u+mu(log||& lowast;u2)u=(e(u2-)1-u2)u,x is an element of R-2, integral R(2)u(2)dx=c, where mu>0,lambda is an element of R , will arise as a Lagrange multiplier and the nonlinearity enjoys critical exponential growth of Trudinger-Moser type. By specifying explicit conditions on the energy level c, we detect a geometry of local minimum and a minimax structure for the corresponding energy functional, and prove the existence of two solutions, one being a local minimizer and one of mountain-pass type. In particular, to catch a second solution of mountain-pass type, some sharp estimates of energy levels are proposed, suggesting a new threshold of compactness in the -constraint. Our study extends and complements the results of Cingolani-Jeanjean (SIAM J Math Anal 51(4): 3533-3568, 2019) dealing with the power nonlinearity a|u|p-2uin the case ofa>0andp>4, in the case of and , which seems to be the first contribution in the context of normalized solutions. Our model presents some new difficulties due to the intricate interplay between a logarithmic convolution potential and a nonlinear term of critical exponential type and requires a novel analysis and the implementation of new ideas, especially in the compactness argument. We believe that our approach will open the door to the study of other -constrained problems with critical exponential growth, and the new underlying ideas are of future development and applicability.

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

306

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

32

Strana od-do

1-32

Kód UT WoS článku

001163818600001

EID výsledku v databázi Scopus

2-s2.0-85183827050