Semiclassical states for fractional logarithmic Schrödinger equations

2020/06/18 by Xiaoming An, An, Xiaoming
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2006.10338

openalex publication_date 2020/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the following fractional logarithmic Schrödinger equation ε^2s(-Δ)^s u + V(x)u=ulog |u|² in \R^N, where ε>0, N≥ 1, V(x)∈ C(\R^N,[-1,+∞)). By introducing an interesting penalized function, we show that the problem has a positive solution u_ε concentrating at a local minimum of V as ε→ 0. There is no restriction on decay rates of V, especially it can be compactly supported.

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