Multi-peak solutions for logarithmic Schrödinger equations with potentials unbounded below

In this paper, we consider the following logarithmic Schrödinger equation$ \begin{equation*} -\varepsilon^2\Delta u + V(x)u = u\log u^2\ \ \text{in}\ {\mathbb R}^N, \end{equation*} $where $ \varepsilon>0 $, N\ge 1 V(x)\in C({\mathbb R}) is a continuous potential which can be unbounded below. By variational methods and penalized idea, show that problem has family of solutions u_{\varepsilon} concentrating at any finite given local minima V $. Our results generalize single peak case in [36] to multi-peak but penalization paper different.