Semiclassical solutions for fractional logarithmic Schrödinger equations with potentials unbounded below - An, Xiaoming; Yang, Xian (Topological Methods in Nonlinear Analysis, 2024)
In this paper, we consider the following fractional logarithmic Schrödinger equation equation* ε^2s(-Δ)^s u + V(x)u=uu^2in ^N, equation* where ε> 0, N1 and V(x)C(^N,) 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_ε concentrating at a local minimum of V as ε→ 0.