Bibliographic Details
| Title: |
Ground states for fractional nonlocal equations with logarithmic nonlinearity |
| Authors: |
Lifeng Guo, Yan Sun, Guannan Shi |
| Source: |
Opuscula Mathematica, Vol 42, Iss 2, Pp 157-178 (2022) |
| Publisher Information: |
AGH Univeristy of Science and Technology Press, 2022. |
| Publication Year: |
2022 |
| Collection: |
LCC:Applied mathematics. Quantitative methods |
| Subject Terms: |
linking theorem, ground state, logarithmic nonlinearity, variational methods, Applied mathematics. Quantitative methods, T57-57.97 |
| More Details: |
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. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
1232-9274 |
| Relation: |
https://www.opuscula.agh.edu.pl/vol42/2/art/opuscula_math_4208.pdf; https://doaj.org/toc/1232-9274 |
| DOI: |
10.7494/OpMath.2022.42.2.157 |
| Access URL: |
https://doaj.org/article/4968dd5983b64e4286bcea15e3024a30 |
| Accession Number: |
edsdoj.4968dd5983b64e4286bcea15e3024a30 |
| Database: |
Directory of Open Access Journals |
