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LI, Y. RADULESCU, V. ZHANG, B.
Original Title
Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration
Type
journal article in Web of Science
Language
English
Original Abstract
In this paper, we are concerned with the study of the following 2-D Schrödinger–Poisson equation with critical exponential growth −ε^2\delta 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.
Keywords
Schrödinger–Poisson system ; Ground state solutions ; Concentration behavior ; Critical exponential growth
Authors
LI, Y.; RADULESCU, V.; ZHANG, B.
Released
30. 5. 2024
Publisher
SPRINGER HEIDELBERG
Location
HEIDELBERG, GERMANY
ISBN
0025-5874
Periodical
MATHEMATISCHE ZEITSCHRIFT
Year of study
307
Number
3
State
Federal Republic of Germany
Pages from
1
Pages to
25
Pages count
URL
https://link.springer.com/article/10.1007/s00209-024-03520-w
BibTex
@article{BUT188818, author="Yiqing {Li} and Vicentiu {Radulescu} and Binlin {Zhang}", title="Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration", journal="MATHEMATISCHE ZEITSCHRIFT", year="2024", volume="307", number="3", pages="1--25", doi="10.1007/s00209-024-03520-w", issn="0025-5874", url="https://link.springer.com/article/10.1007/s00209-024-03520-w" }