NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R<SUP>2</SUP>

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F23%3APU150392" target="_blank" >RIV/00216305:26220/23:PU150392 - isvavai.cz</a>

Výsledek na webu

<a href="https://epubs.siam.org/doi/10.1137/22M1521675" target="_blank" >https://epubs.siam.org/doi/10.1137/22M1521675</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/22M1521675" target="_blank" >10.1137/22M1521675</a>

Jazyk výsledku

angličtina

Název v původním jazyce

NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R<SUP>2</SUP>

Popis výsledku v původním jazyce

For any a > 0, we study the existence of normalized solutions and ground state solutions to the following Schrodinger equation with L-2-constraint: { -Delta u + lambda u = b(x)f(u) x is an element of R-2, integral(2)(R) u(2)dx = a, where lambda is an element of R is a Lagrange multiplier, the potential b is an element of C(R-2, (0, infinity)) satisfies 0 < lim(|y|->infinity) b(y) <= inf(x is an element of)R(2) b(x) and appears as a converse direction of the Rabinowitz-type trapping potential, and the reaction f is an element of C(R, R) enjoys critical exponential growth of Trudinger-Moser type. Under two different kinds of assumptions on f, we prove several new existence results, which, in the context of normalized solutions, can be considered as both counterparts of planar unconstrained critical problems and extensions of unconstrained Schrodinger problems with Rabinowitz-type trapping potential. Especially, in this scenario, we develop some sharp estimates of energy levels and ingenious analysis techniques to restore the compactness which are novel even for b(x) equivalent to constant. We believe that these techniques will allow not only treating other L-2-constrained problems in the Trudinger-Moser critical setting but also generalizing previous results to the case of variable potentials.

Název v anglickém jazyce

NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R<SUP>2</SUP>

Popis výsledku anglicky

For any a > 0, we study the existence of normalized solutions and ground state solutions to the following Schrodinger equation with L-2-constraint: { -Delta u + lambda u = b(x)f(u) x is an element of R-2, integral(2)(R) u(2)dx = a, where lambda is an element of R is a Lagrange multiplier, the potential b is an element of C(R-2, (0, infinity)) satisfies 0 < lim(|y|->infinity) b(y) <= inf(x is an element of)R(2) b(x) and appears as a converse direction of the Rabinowitz-type trapping potential, and the reaction f is an element of C(R, R) enjoys critical exponential growth of Trudinger-Moser type. Under two different kinds of assumptions on f, we prove several new existence results, which, in the context of normalized solutions, can be considered as both counterparts of planar unconstrained critical problems and extensions of unconstrained Schrodinger problems with Rabinowitz-type trapping potential. Especially, in this scenario, we develop some sharp estimates of energy levels and ingenious analysis techniques to restore the compactness which are novel even for b(x) equivalent to constant. We believe that these techniques will allow not only treating other L-2-constrained problems in the Trudinger-Moser critical setting but also generalizing previous results to the case of variable potentials.

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

2023

Kód důvěrnosti údajů

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

Název periodika

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

ISSN

0036-1410

e-ISSN

1095-7154

Svazek periodika

55

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

37

Strana od-do

7704-7740

Kód UT WoS článku

001114759300005

EID výsledku v databázi Scopus

2-s2.0-85182455753