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Symmetry of standing waves for two kinds of fractional Hardy-Schrödinger equations
Journal article   Open access  Peer reviewed

Symmetry of standing waves for two kinds of fractional Hardy-Schrödinger equations

Guotao Wang, Xueyan Ren, Lihong Zhang and Bashir Ahmad
Alexandria engineering journal, Vol.60(4), pp.3991-3995
08/2021
DOI: https://doi.org/10.1016/j.aej.2021.02.023

Abstract

Direct method of moving planes Generalized Hartree-type fractional Hardy-Schrödinger equation Generalized Pekar-Choquard type fractional Hardy-Schrödinger equation Radial symmetry Standing waves
In this paper, we consider two kinds of nonlinear Schrödinger equations with the fractional Laplacian and Hardy potential (λ|x|s, 0<λ⩽λ∗,λ∗ is a constant of the Hardy-Sobolev inequality), which represent the generalized form of Hartree and Pekar-Choquard type time dependent fractional Hardy-Schrödinger equations. Applying the direct method of moving planes, we obtain the radial symmetry and monotonicity of the standing waves for the given equations.
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https://doi.org/10.1016/j.aej.2021.02.023View
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