Detail publikace

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

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

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

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

Vydáno

18. 10. 2023

ISSN

1007-5704

Periodikum

Communications in Nonlinear Science and Numerical Simulation

Ročník

2023(125)

Číslo

107418

Stát

Nizozemsko

Strany od

1

Strany do

19

Strany počet

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"
}