Normalized bound state solutions for the fractional Schrödinger equation with potential

2023/07/16 by Xin Bao, Bao, Xin, Ying Lv +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2307.07927

openalex publication_date 2023/07/16 · openalex created_date 2023/07/19 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the following fractional Schrödinger equation with prescribed mass \ \beginaligned amp;(-Δ)^su=λu+a(x)|u|^p-2u, \textin ℝ^N,
amp;∫_ℝ^N|u|²dx=c², u∈ H^s(ℝ^N), \endaligned . where 02s, 2+(4s)/(N)0, λ∈ ℝ and a(x)∈ C¹(ℝ^N,ℝ⁺) is a potential function. By using a minimax principle, we prove the existence of bounded state normalized solution under various conditions on a(x).

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