Multi-bump positive solutions for a logarithmic Schrödinger equation with deepening potential well.

This article concerns the existence of multi-bump positive solutions for the following logarithmic Schrödinger equation: { u + V (x) u = u log u 2 i n R N , u H 1 (R N) , where N ⩾ 1, ⋋ > 0 is a parameter and the nonnegative continuous function V: ℝ^N → ℝ has potential well Ω:= int V⁻¹(0) which possesses k disjoint bounded components Ω= ∪ j = 1 k Ω j . Using the variational methods, we prove that if the parameter ⋋ > 0 is large enough, then the equation has at least 2^k − 1 multi-bump positive solutions. [ABSTRACT FROM AUTHOR]