Detail publikačního výsledku

Multiple normalized solutions for fractional elliptic problems

NGUYEN, T.; RADULESCU, V.

Originální název

Multiple normalized solutions for fractional elliptic problems

Anglický název

Multiple normalized solutions for fractional elliptic problems

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

NGUYEN, T.; RADULESCU, V.

Rok RIV

2025

Vydáno

02.09.2024

ISSN

0933-7741

Periodikum

FORUM MATHEMATICUM

Svazek

36

Číslo

5

Stát

Spolková republika Německo

Strany od

1225

Strany do

1248

Strany počet

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"
}