Normalized bound state solutions of fractional Schrödinger equations with general potential

2023/07/14 by Xin Bao, Bao, Xin, Ying Lv +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2307.07379

openalex publication_date 2023/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a class of fractional Schrödinger equation \ \beginaligned amp;(-Δ)^su=λu+a(x)|u|^p-2u,
amp;∫_ℝ^N|u|²dx=c², u∈ H^s(ℝ^N), \endaligned . where N>2s, s∈(0,1) and p∈(2,2+4s/N), c>0. a(x)∈ C(ℝ^N,ℝ) is a positive potential function. By using Fixed Point Theorem of Brouwer, barycenter function and variational method, we obtain the existence of normalized bound solutions for the problem.

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