Publication detail

Convergence of least energy sign-changing solutions for logarithmic Schrödinger equations on locally finite graphs

CHANG, X. RADULESCU, V. WANG, R. YAN, D.

Original Title

Convergence of least energy sign-changing solutions for logarithmic Schrödinger equations on locally finite graphs

Type

journal article in Web of Science

Language

English

Original Abstract

In this paper, we study the following logarithmic Schrödinger equation $−\Delta u+λa(x)u=u\logu^2 $ in V on a connected locally finite graph $G=(V,E)$, where $\Delta$ denotes the graph Laplacian, λ>0 is a constant, and a(x)≥0 represents the potential. Using variational techniques in combination with the Nehari manifold method based on directional derivative, we can prove that, there exists a constant $λ_0>0$ such that for all $λ≥λ_0$, the above problem admits a least energy sign-changing solution $u_λ$. Moreover, as λ→+∞, we prove that the solution $u_λ$ converges to a least energy sign-changing solution of the following Dirichlet problem $−\Delta u=ulogu^2 $ in Ω, u(x)=0 on ∂Ω, where Ω={x∈V:a(x)=0} is the potential well.

Keywords

Least energy sign-changing solutions; Locally finite graphs; Logarithmic Schrödinger equations; Nehari manifold method

Authors

CHANG, X.; RADULESCU, V.; WANG, R.; YAN, D.

Released

18. 10. 2023

ISBN

1007-5704

Periodical

Communications in Nonlinear Science and Numerical Simulation

Year of study

2023(125)

Number

107418

State

Kingdom of the Netherlands

Pages from

1

Pages to

19

Pages count

19

URL

https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001047668700001

BibTex

@article{BUT184212,
  author="Xiaojun {Chang} and Vicentiu {Radulescu} and Ru {Wang} and Duokui {Yan}",
  title="Convergence of least energy sign-changing solutions for logarithmic Schrödinger equations on locally finite graphs",
  journal="Communications in Nonlinear Science and Numerical Simulation",
  year="2023",
  volume="2023(125)",
  number="107418",
  pages="1--19",
  doi="10.1016/j.cnsns.2023.107418",
  issn="1007-5704",
  url="https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001047668700001"
}