Open AccessGround states for fractional nonlocal equations with logarithmic nonlinearity
Author(s) -
Lei Guo,
Yan Sun,
Guannan Shi
Publication year - 2022
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2022.42.2.157
Subject(s) - omega , bounded function , lipschitz continuity , logarithm , ground state , operator (biology) , sobolev space , nonlinear system , boundary (topology) , physics , open set , state (computer science) , mathematics , lipschitz domain , mathematical physics , pure mathematics , mathematical analysis , quantum mechanics , biochemistry , chemistry , repressor , algorithm , transcription factor , gene
In this paper, we study on the fractional nonlocal equation with the logarithmic nonlinearity formed by \[\begin{cases}\mathcal{L}_{K}u(x)+u\log|u|+|u|^{q-2}u=0, & x\in\Omega,\\ u=0, & x\in\mathbb{R}^{n}\setminus\Omega,\end{cases}\] where \(2\lt q\lt 2^{*}_s\), \(L_{K}\) is a non-local operator, \(\Omega\) is an open bounded set of \(\mathbb{R}^{n}\) with Lipschitz boundary. By using the fractional logarithmic Sobolev inequality and the linking theorem, we present the existence theorem of the ground state solutions for this nonlocal problem.