Publication detail

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

NGUYEN, T. RADULESCU, V.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

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

Authors

NGUYEN, T.; RADULESCU, V.

Released

25. 1. 2023

ISBN

0025-2611

Periodical

MANUSCRIPTA MATHEMATICA

Year of study

173

Number

1-2

State

Federal Republic of Germany

Pages from

499

Pages to

554

Pages count

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"
}