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

In this paper, we consider the following logarithmic Schrödinger equation) is a continuous potential which can be unbounded below.By variational methods and penalized idea, we show that the problem has a family of solutions uε concentrating at any finite given local minima of V .Our results generalize the single peak case in [36] to the multi-peak case but the penalization in this paper is different.