@article{An_Yang_2024, title={Semiclassical solutions for fractional logarithmic Schrödinger equations with potentials unbounded below}, url={https://apcz.umk.pl/TMNA/article/view/55336}, DOI={10.12775/TMNA.2023.063}, abstractNote={In this paper, we consider the following fractional logarithmic Schrödinger equation
\begin{equation*}
\varepsilon^{2s}(-\Delta)^s u + V(x)u=u\log u^2\quad \text{in } \R^N,
\end{equation*}
where $\varepsilon> 0$, $N\ge 1$ and $V(x)\in C\big(\R^N,\R\big)$ is a potential which can be unbounded below at infinity.
By considering a new penalization, we show that the problem has a nontrivial solution $u_{\varepsilon}$ concentrating at a local minimum of $V$
as $\varepsilon\to 0$.}, journal={Topological Methods in Nonlinear Analysis}, author={An, Xiaoming and Yang, Xian}, year={2024}, month={Sep.}, pages={1–25} }