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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

MATHEMATISCHE ZEITSCHRIFT

ISSN

0025-5874

e-ISSN

1432-8232

Volume of the periodical

306

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

32

Pages from-to

1-32

UT code for WoS article

001163818600001

EID of the result in the Scopus database

2-s2.0-85183827050