Existence and concentration of positive solutions for a logarithmic Schrödinger equation via penalization method

2019/06/18 by Alves, Claudianor O., Ji, Chao · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.07454

Abstract

In this article we are concerned with the following logarithmic Schrödinger equation \ -ε²Δu+ V(x)u=u log u², · amp; in ℝ^N,
%u(x) · gt;0, · amp; in ℝ^N
u ∈ H¹(ℝ^N), · amp; . where ε>0, N ≥ 1 and V:ℝ^N→ ℝ is a continuous potential. Under a local assumption on the potential V, we use the variational methods to prove the existence and concentration of positive solutions for the above problem.

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