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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
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" }