Compact embeddings for weighted fractional Sobolev spaces and applications to Nonlinear Schrödinger Equations

2023/08/04 by Federico Bernini, Bernini, Federico, Sergio Rolando +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2308.02311

openalex publication_date 2023/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions for the following Schrödinger equation (-Δ)^su + V(|x|)u = K(|x|)f(u), in ℝ^N, where the two measurable functions K > 0 and V ≥ 0 could vanish at infinity.

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