Publication detail

Multiple normalized solutions for fractional elliptic problems

NGUYEN, T. RADULESCU, V.

Original Title

Multiple normalized solutions for fractional elliptic problems

Type

journal article in Web of Science

Language

English

Original Abstract

In this article, we are first concerned with the existence of multiple normalized solutions to the following fractional p-Laplace problem:{(-Delta)(p)(s)v + V(xi(x))|v|(p-2)v = lambda|v|(p-2)v + f(v) in R-N, integral(N)(R) |v|(p )dx = a(p),where a, xi > 0, p >= 2, lambda is an element of R is an unknown parameter that appears as a Lagrange multiplier, V : R-N -> [0, infinity) is a continuous function, and f is a continuous function with L-p-subcritical growth. We prove that there exists the multiplicity of solutions by using the Lusternik-Schnirelmann category. Next, we show that the number of normalized solutions is at least the number of global minimum points of V, as xi is small enough via Ekeland's variational principle.

Keywords

Lusternik-Schnirelmann category;normalized solutions;nonlinear Schrodinger equation;variational methods

Authors

NGUYEN, T.; RADULESCU, V.

Released

2. 9. 2024

ISBN

0933-7741

Periodical

FORUM MATHEMATICUM

Year of study

36

Number

5

State

Federal Republic of Germany

Pages from

1225

Pages to

1248

Pages count

24

URL

https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001141871200001

BibTex

@article{BUT187378,
  author="Thin  Van {Nguyen} and Vicentiu {Radulescu}",
  title="Multiple normalized solutions for fractional elliptic problems",
  journal="FORUM MATHEMATICUM",
  year="2024",
  volume="36",
  number="5",
  pages="1225--1248",
  doi="10.1515/forum-2023-0366",
  issn="0933-7741",
  url="https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001141871200001"
}