- Tytuł:
- Ground states for fractional nonlocal equations with logarithmic nonlinearity
- Autorzy:
-
Guo, Lifeng
Sun, Yan
Shi, Guannan - Powiązania:
- https://bibliotekanauki.pl/articles/2048894.pdf
- Data publikacji:
- 2022
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
linking theorem
ground state
logarithmic nonlinearity
variational methods - Opis:
- In this paper, we study on the fractional nonlocal equation with the logarithmic nonlinearity formed by $$\begin{cases}\mathcal{L}_{K} u(x)+u \log |u|+|u|^{q-2} u=0, & x \in \Omega \\ u=0, & x \in \mathbb{R}^{n} \backslash \Omega\end{cases}$$ where 2 < q < 2∗s, LK is a non-local operator, Ω is an open bounded set of Rn 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.
- Źródło:
-
Opuscula Mathematica; 2022, 42, 2; 157-178
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł