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:{−Δu+λV(x)u=ulogu^(2)inRN,u∈H^(1)(R^(N)),where N≥1,⋋>0 is a parameter and the nonnegative continuous function V:ℝ^(N)→ℝhas potential wellΩ:=int V^(−1)(0)which possesses k disjoint bounded componentsΩ=∪^(k)_(j)=1Ω_(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.