Open AccessPositive solutions for the fractional Schrödinger equations with logarithmic and critical non‐linearities
Author(s) -
Fan Haining,
Feng Zhaosheng,
Yan Xingjie
Publication year - 2021
Publication title -
transactions of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.43
H-Index - 7
ISSN - 2052-4986
DOI - 10.1112/tlm3.12034
Subject(s) - nehari manifold , mathematics , logarithm , multiplicity (mathematics) , sign (mathematics) , schrödinger equation , domain (mathematical analysis) , ground state , mathematical analysis , pure mathematics , nonlinear system , physics , quantum mechanics
In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non‐linearities on an unbounded domain, and show that such an equation with positive or sign‐changing weight potentials admits at least one positive ground state solution and the associated energy is positive (or negative). By applying the Nehari manifold method and Ljusternik–Schnirelmann category, we investigate how the weight potential affects the multiplicity of positive solutions, and obtain the relationship between the number of positive solutions and the category of some sets related to the weight potential.