Remarks on nondegeneracy of ground states for quasilinear Schrödinger equations

Chang-Lin  Xiang

doi:10.3934/dcds.2016054

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2016, Volume 36, Issue 10: 5789-5800. Doi: 10.3934/dcds.2016054

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Remarks on nondegeneracy of ground states for quasilinear Schrödinger equations

Chang-Lin Xiang^1,

1.
University of Jyvaskyla, Department of Mathematics and Statistics, P.O. Box 35, FI-40014 University of Jyvaskyla

Received: August 31, 2015

Revised: February 29, 2016

Published: May 2017

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Abstract

In this paper, we answer affirmatively the problem proposed by A. Selvitella in his work "Nondegeneracy of the ground state for quasilinear Schrödinger equations" (see Calc. Var. Partial Differential Equations, 53 (2015), 349-364): every ground state of the quasilinear Schrödinger equation \begin{eqnarray*}-\Delta u-u\Delta |u|^2+\omega u-|u|^{p-1}u=0&&\text{in }\mathbb{R}^N\end{eqnarray*} is nondegenerate for $1< p <3$, where $\omega > 0$ is a given constant and $N \ge1$.

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Mathematics Subject Classification: Primary: 35J62, 35Q55; Secondary: 35J60.

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