Remarks on Nondegeneracy of Ground States for Quasilinear Schrödinger Equations

2015/06/11 by Chang‐Lin Xiang, Xiang, Chang-Lin
Mathematics · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35J62 #Secondary 35J60 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1506.03628

openalex publication_date 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we answer affirmatively the problem proposed by A. Selvitella in his paper "Nondegenracy of the ground state for quasilinear Schrödinger Equations" (see Calc. Var. Partial Differ. Equ., \bf 53 (2015), pp 349-364): every ground state of equation -Δu-uΔ|u|²+ωu-|u|^p-1u=0amp;amp;in ℝ^N is nondegenerate for 10 is a given constant and N≥1. We also derive further properties on the linear operator associated to ground states of above equation.

Citations

• Uniqueness of positive solutions of Δu−u+up=0 in Rn
• Uniqueness of Radial Solutions for the Fractional Laplacian

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