Existence and Stability of Standing Waves for the Inhomogeneous Schrödinger Equations with Mixed Fractional Laplacians
Year: 2025
Type: article
Abstract: In this paper, we consider the existence and orbital stability of standing waves for the inhomogeneous Schrödinger equations with mixed fractional Laplacians i ∂ t ψ− ( −Δ ) s 1 ψ− ( −Δ ) s 2 ψ+ | x | −γ | ψ | 2σ ψ=0, ( t,x )∈[ 0,T )× ℝ N , where N≥2 , 0 s 2 s 1 1 , and 0γ2 s 1 . In the L 2 -subcritical case, i.e., 0σ 2 s 1 −γ N , we establish the existence and orbital stability of standing waves. Our approach is based on the concentration-compactness principle in the fractional Sobolev spaces H s 1 for s 1 ∈( 0,1 ) .
Author: Wenlong Du
Institution: Northwest Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409521359