TY  - JOUR
ID  - Guo2022
LB  - Guo2022
AU  - Guo, Lifeng
AU  - Sun, Yan
AU  - Shi, Guannan
TI  - Ground states for fractional nonlocal equations with logarithmic nonlinearity
ST  - Ground states for fractional nonlocal equations with logarithmic nonlinearity
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 2
SP  - 157
EP  - 178
DO  - https://doi.org/10.7494/OpMath.2022.42.2.157
UR  - https://doi.org/10.7494/OpMath.2022.42.2.157
AB  - 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.
KW  - linking theorem
KW  - ground state
KW  - logarithmic nonlinearity
KW  - variational methods
SN  - 1232-9274
ER  -