Publication detail

Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction

SHUAI, Y. RADULESCU, V. TANG, X. ZHANG, L.

Original Title

Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction

Type

journal article in Web of Science

Language

English

Original Abstract

This paper is concerned with the following fractional (N/s)-Laplacian Choquard equation: epsilon(N )(-Delta)(s)(N/s)u + V(x)|u|(N/s-2)u = epsilon(mu)(1 / |x|(N-mu )& lowast;F(u) )f(u), x is an element of R-N,where (-Delta)(s)(N/s) denotes the (N/s)-Laplacian operator, 0 < mu < N, and V and f are continuous real functions satisfying some mild assumptions. Applying the weak growth conditions on the exponential critical nonlinearity f and without using the strictly monotone condition, we use some refined analysis and develop the arguments in the existing results to establish the existence of the ground state solution of the fractional (N/s)-Laplacian Choquard equation. Moreover, we also study the concentration phenomenon of the ground state solutions. As far as we know, our results seem to be new concerning the fractional (N/s)-Laplacian equation with the Choquard reaction.

Keywords

NONLINEAR SCHRODINGER-EQUATIONS;GROUND-STATE SOLUTIONS; CHOQUARD EQUATION; CONCENTRATION BEHAVIOR; WEAK SOLUTIONS; MULTIPLICITY; EXISTENCE; INEQUALITY; CONSTANT; FIELD

Authors

SHUAI, Y.; RADULESCU, V.; TANG, X.; ZHANG, L.

Released

1. 5. 2024

ISBN

0933-7741

Periodical

FORUM MATHEMATICUM

Year of study

36

Number

3

State

Federal Republic of Germany

Pages from

783

Pages to

810

Pages count

28

URL

https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001089369200001

BibTex

@article{BUT185747,
  author="Yuan {Shuai} and Vicentiu {Radulescu} and Xianhua {Tang} and Limin {Zhang}",
  title="Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction",
  journal="FORUM MATHEMATICUM",
  year="2024",
  volume="36",
  number="3",
  pages="783--810",
  doi="10.1515/forum-2023-0183",
  issn="0933-7741",
  url="https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001089369200001"
}