Detail publikace

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

LI, Y. RADULESCU, V. ZHANG, B.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

Schrödinger–Poisson system ; Ground state solutions ; Concentration behavior ; Critical exponential growth

Autoři

LI, Y.; RADULESCU, V.; ZHANG, B.

Vydáno

30. 5. 2024

Nakladatel

SPRINGER HEIDELBERG

Místo

HEIDELBERG, GERMANY

ISSN

0025-5874

Periodikum

MATHEMATISCHE ZEITSCHRIFT

Ročník

307

Číslo

3

Stát

Spolková republika Německo

Strany od

1

Strany do

25

Strany počet

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"
}