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Lack of Ground State for NLSE on Bridge-Type Graphs

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Mathematical Technology of Networks

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 128))

Abstract

We prove the nonexistence of ground states for NLSE on bridge-like graphs, i.e. graphs with two halflines and four vertices, of which two at infinity, with Kirchhoff matching conditions. By ground state we mean any minimizer of the energy functional among all functions with the same mass.

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Notes

  1. 1.

    Contribution for the proceedings of the Workshop on “Mathematical Technology of Networks”, ZiF Bielefeld, 4-7 December 2013.

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Acknowledgements

R.A. and E.S. are partially supported by the PRIN 2012 project “Aspetti variazionali e perturbativi nei problemi differenziali nonlineari”. R.A. is partially supported by the FIRB 2012 project “Dispersive dynamics: Fourier Analysis and Variational Methods”.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche G.L. Lagrange, Politecnico di Torino, Torino, Italy

    Riccardo Adami, Enrico Serra & Paolo Tilli

Authors
  1. Riccardo Adami
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  2. Enrico Serra
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  3. Paolo Tilli
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Corresponding author

Correspondence to Riccardo Adami .

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Editors and Affiliations

  1. Lehrgebiet Analysis, FernUniversität in Hagen, Hagen, Germany

    Delio Mugnolo

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Adami, R., Serra, E., Tilli, P. (2015). Lack of Ground State for NLSE on Bridge-Type Graphs. In: Mugnolo, D. (eds) Mathematical Technology of Networks. Springer Proceedings in Mathematics & Statistics, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-319-16619-3_1

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