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Dipierro, S. and Valdinoci, E. (2021) Description of an Ecological Niche for a Mixed Local/Nonlocal Dispersal: An Evolution Equation and a New Neumann Condition Arising from the Superposition of Brownian and Lévy Processes. Physica A: Statistical Mechanics and Its Applications, 575, Article 126052.
https://doi.org/10.1016/j.physa.2021.126052

has been cited by the following article:

• TITLE: Existence and Stability of Standing Waves for the Inhomogeneous Schrödinger Equations with Mixed Fractional Laplacians

  AUTHORS: Wenlong Du

  KEYWORDS: Laplace Operator, Existence, Stability

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.4, April 17, 2025

  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 0<γ<2 s 1 . In the L 2 -subcritical case, i.e., 0<σ< 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 ) .