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Nondegeneracy of the ground state for quasilinear Schrödinger equations

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Abstract

We study least energy solutions for a class of quasilinear Schrödinger equations and we prove that the ground states are non degenerate. We also explain how close the proof of nondegeneracy and our argument are to the proof of uniqueness of the ground state up to symmetries.

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Acknowledgments

We would like to thank Prof. Louis Jeanjean for having proposed me to study this problem. We would like also to thank him for a lot of useful comments, in particular for an important correction in the proof of Proposition 3.10. We would like to thank for the kind hospitality the Laboratoire de Mathématiques of the Université de Franche-Comté in Besancon, where this research started and in particular Dr.Nabile Boussaid. We thank Prof.Andrea Malchiodi for his advice and useful comments. We thank also the anonymous referee for his comments which led to an improvement of this manuscript. We thank also Victoria Ban for her kindness and constant help.

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  1. Department of Mathematics and Statistics, McMaster University, 1280 Main Street, West Hamilton ON L8S 4K1, Canada

    Alessandro Selvitella

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  1. Alessandro Selvitella
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Correspondence to Alessandro Selvitella.

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Communicated by A. Malchiodi.

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Selvitella, A. Nondegeneracy of the ground state for quasilinear Schrödinger equations. Calc. Var. 53, 349–364 (2015). https://doi.org/10.1007/s00526-014-0751-8

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