Detail publikace

Multiplicity and concentration of solutions to fractional anisotropic Schrodinger equations with exponential growth

NGUYEN, T. RADULESCU, V.

Originální název

Multiplicity and concentration of solutions to fractional anisotropic Schrodinger equations with exponential growth

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

In this paper, we consider the Schrodinger equation involving the fractional $(p, p_1, . . . , p_m)$-Laplacian as follows $(-Delta)_p^s u +\sum_ {i=1}^m (-\Delta)_{p_i}^s u + V(\epsilon x)(|u|^{(N-2s)/2s} u + sum_{i=1}^m |u|^{p_i-2} u) = f (u) \in R^N$ where $\epsilon$ is a positive parameter, $N=ps, s \in (0,1), 2 \leq p < p_1 < \dots < p_m < +\infty, m \geq 1$. The nonlinear function f has the exponential growth and potential function V is continuous function satisfying some suitable conditions. Using the penalization method and Ljusternik-Schnirelmann theory, we study the existence, multiplicity and concentration of nontrivial nonnegative solutions for small values of the parameter. In our best knowledge, it is the first time that the above problem is studied.

Klíčová slova

MOSER-TRUDINGER INEQUALITY;SOBOLEV-SLOBODECKIJ SPACES;POSITIVE SOLUTIONS;ELLIPTIC-EQUATIONS;EXISTENCE;DIMENSION;SYSTEMS;STATES

Autoři

NGUYEN, T.; RADULESCU, V.

Vydáno

25. 1. 2023

ISSN

0025-2611

Periodikum

MANUSCRIPTA MATHEMATICA

Ročník

173

Číslo

1-2

Stát

Spolková republika Německo

Strany od

499

Strany do

554

Strany počet

56

URL

https://link.springer.com/article/10.1007/s00229-022-01450-7

BibTex

@article{BUT184005,
  author="Thin  Van {Nguyen} and Vicentiu {Radulescu}",
  title="Multiplicity and concentration of solutions to fractional anisotropic Schrodinger equations with exponential growth",
  journal="MANUSCRIPTA MATHEMATICA",
  year="2023",
  volume="173",
  number="1-2",
  pages="499--554",
  doi="10.1007/s00229-022-01450-7",
  issn="0025-2611",
  url="https://link.springer.com/article/10.1007/s00229-022-01450-7"
}