NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R<SUP>2</SUP>
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
NORMALIZED SOLUTIONS FOR SCHRODINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH IN R<SUP>2</SUP>
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN
0036-1410
e-ISSN
1095-7154
Volume of the periodical
55
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
37
Pages from-to
7704-7740
UT code for WoS article
001114759300005
EID of the result in the Scopus database
2-s2.0-85182455753