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Stable solutions to quasilinear Schrödinger equations of Lane–Emden type with a parameter
Author(s) -
Wei Yunfeng,
Yang Hongwei,
Yu Hongwang,
Hu Rui
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7385
Subject(s) - mathematics , bounded function , type (biology) , sign (mathematics) , class (philosophy) , mathematical analysis , function (biology) , comparison theorem , mathematical physics , pure mathematics , ecology , artificial intelligence , evolutionary biology , computer science , biology
In this paper, we study the following quasilinear Schrödinger equations− Δ u − Δ ( | u | 2 α ) | u | 2 α − 2 u = ω ( x ) | u | q − 1 u , x ∈ ℝ N , where α > 1 2is a parameter, q > 3 α − 1 + α 2 α , ω ( x ) ∈ C ( ℝ N \ { 0 } ) is a positive function. We establish a Liouville type theorem for the class of stable bounded sign‐changing solutions under suitable assumptions on ω ( x ), q , α and N .