On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in ℝ N

On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in ℝ N

We study an eigenvalue problem for functions in ℝ N and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability of the standing waves of the nonlinear Schrödinger equation.

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Veröffentlicht in:Advanced nonlinear studies 2007-08, Vol.7 (3), p.439-458
Hauptverfasser: Bellazzini, J., Ghimenti, V. Benci M., Micheletti, A.M.
Format: Artikel
Sprache:eng
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Zusammenfassung:We study an eigenvalue problem for functions in ℝ N and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability of the standing waves of the nonlinear Schrödinger equation.
ISSN:1536-1365
2169-0375
DOI:10.1515/ans-2007-0306