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On the finiteness of the Morse index for Schrödinger operators

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Abstract

We show that if M is a complete Riemannian manifold and H = Δ + V is a Schrödinger operator, then the existence of a positive solution of Hu = 0 outside a compact set is equivalent to the finiteness of the Morse index of H.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Jean Leray, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322, Nantes Cedex 03, France

    Baptiste Devyver

  2. Department of Mathematics, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Baptiste Devyver

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  1. Baptiste Devyver
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Correspondence to Baptiste Devyver.

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Devyver, B. On the finiteness of the Morse index for Schrödinger operators. manuscripta math. 139, 249–271 (2012). https://doi.org/10.1007/s00229-011-0522-1

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  • DOI: https://doi.org/10.1007/s00229-011-0522-1

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