Semiclassical solutions for fractional logarithmic Schrödinger equations with potentials unbounded below

In this paper, we consider the following fractional logarithmic Schrödinger equation {equation*} ε²ˢ(-Δ)^s u + V(x)u=ulog u^2 in ^N, {equation*} where ε> 0, N≥ 1 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 uε concentrating at a local minimum of V as ε→ 0.