Publication detail

Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration

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

25

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"
}