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Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

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Abstract

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the “band tails.” Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.

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References

  1. Albanese, C., Fröhlich, J.: Periodic solutions of some infinite dimensional Hamiltonian systems associated with partial difference equations. Commun. Math. Phys.116, 475–502 (1988)

    Google Scholar 

  2. Rabinowitz, P.: Some global results for non-linear eigenvalue problems. J. Funct. Anal.7, 487–513 (1971)

    Google Scholar 

  3. Albanese, C.: A continuation method for non-linear eigenvalue problem. J. Funct. Anal. (in press)

  4. Albanese, C.: Localised solutions of Hartree equations for narrow band crystals. Commun. Math. Phys. (in press)

  5. Wegner, F.: Bounds on the density of states for disordered systems. Z. Phys. B22, 9 (1981)

    Google Scholar 

  6. Fröhlich, J., Spencer, T.: Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Commun. Math. Phys.88, 151 (1983)

    Google Scholar 

  7. Simon, B.: Correlation inequalities and the decay of correlations in ferromagnets. Commun. Math. Phys.77, 111 (1980)

    Google Scholar 

  8. Chow, S.N., Hale, J.K.: Methods of bifurcation theory. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

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Author notes

  1. Claudio Albanese

    Present address: Department of Mathematics, University of California, 90024, Los Angeles, CA, USA

Authors and Affiliations

  1. Theoretical Physics, ETH-Hönggerberg, CH-8093, Zürich, Switzerland

    Claudio Albanese & Jürg Fröhlich

  2. The Institute for Advanced Study, 08540, Princeton, NJ, USA

    Thomas Spencer

Authors
  1. Claudio Albanese
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  2. Jürg Fröhlich
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  3. Thomas Spencer
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Communicated by A. Jaffe

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Albanese, C., Fröhlich, J. & Spencer, T. Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II. Commun.Math. Phys. 119, 677–699 (1988). https://doi.org/10.1007/BF01218350

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  • DOI: https://doi.org/10.1007/BF01218350

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