@Article{Guo2022,
author = "Guo, Lifeng and Sun, Yan and Shi, Guannan",
title = "Ground states for fractional nonlocal equations with logarithmic nonlinearity",
journal = "Opuscula Math.",
year = "2022",
volume = "42",
number = "2",
pages = "157--178",
doi = "https://doi.org/10.7494/OpMath.2022.42.2.157",
url = "https://doi.org/10.7494/OpMath.2022.42.2.157",
abstract = "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.",
keywords = "linking theorem, ground state, logarithmic nonlinearity, variational methods",
issn = "1232-9274"
}