Multi-bump solutions for logarithmic Schrödinger equations

2016/08/05 by Tanaka, Kazunaga, Zhang, Chengxiang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.01742

Abstract

We study spatially periodic logarithmic Schrödinger equations: -Δu + V(x)u=Q(x)ulog u², ugt;0 in ℝ^N, where N≥ 1 and V(x), Q(x) are spatially 1-periodic functions of class C¹. We take an approach using spatially 2L-periodic problems (L≫ 1) and we show the existence of infinitely many multi-bump solutions of (LS) which are distinct under ℤ^N-action.

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