Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
MATHEMATISCHE ZEITSCHRIFT
ISSN
0025-5874
e-ISSN
1432-8232
Volume of the periodical
307
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
25
Pages from-to
1-25
UT code for WoS article
001238245700005
EID of the result in the Scopus database
2-s2.0-85195398625