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Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity

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References

  1. A. Ambrosetti and M. Badiale,Homoclinics: Poincaré-Melnikov type results via a variational approach, Ann. Inst. H. Poincaré Anal. Non Linéaire15 (1998), 233–252.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Ambrosetti and A. Malchiodi,Perturbation Methods and Semilinear Elliptic Problems on ℝ n, Progress in mathematics, Vol. 240, Birkhäuser, Basel, 2005.

    Google Scholar 

  3. A. Ambrosetti, V. Felli and A. Malchiodi,Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity, J. European Math. Soc.7 (2005), 117–144.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Ambrosetti, A. Malchiodi and W.-M. Ni,Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, Part I, Comm. Math. Phys.235 (2003), 427–466.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Ambrosetti, A. Malchiodi and S. Secchi,Multiplicity results for some nonlinear singularly perturbed elliptic problems on R n, Arch. Rational Mech. Anal.159 (2001), 253–271.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Bahri and P. L. Lions,On the existence of a positive solution of semilinear elliptic equations in unbounded domains, Ann. Inst. H. Poincaré Anal. Non Linéaire14 (1997), 365–413.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Chabrowski,Variational Methods for Potential Operator Equations. With Applications to Nonlinear Elliptic Equations, Walter de Gruyter & Co., Berlin, 1997.

    MATH  Google Scholar 

  8. D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Second edition, Springer-Verlag, Berlin, 1983.

    MATH  Google Scholar 

  9. N. K. Kwong,Uniqueness of positive solutions of Δu−u+u p =0 in ℝ n, Arch. Rational Mech. Anal.105 (1989), 243–266.

    Article  MATH  MathSciNet  Google Scholar 

  10. N. N. Lebedev,Special Functions and their Applications, Prentice Hall, Inc., Englewood Cliffs, N.J., 1965.

    MATH  Google Scholar 

  11. E. S. Noussair and C. A. Swanson,Decaying solutions of semilinear elliptic equations in ℝ n, SIAM J. Math. Anal.20 (1989), 1336–1343.

    Article  MATH  MathSciNet  Google Scholar 

  12. Y-G. Oh,On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potentials, Comm. Math. Phys.131 (1990), 223–253.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. H. Rabinowitz,On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys.43 (1992), 270–291.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Schneider,Entire solutions of semilinear elliptic problems with indefinite nonlinearities, PhD Thesis, Universität Mainz, 2001.

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Authors and Affiliations

  1. S.I.S.S.A., 2-4 via Beirut, 34014, Trieste, Italy

    A. Ambrosetti & A. Malchiodi

  2. Department of Mathematical Analysis, University of Granada, Granada, Spain

    D. Ruiz

Authors
  1. A. Ambrosetti
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  2. A. Malchiodi
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  3. D. Ruiz
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Correspondence to A. Ambrosetti.

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Part of the work was carried out during some visits at S.I.S.S.A.

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Ambrosetti, A., Malchiodi, A. & Ruiz, D. Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity. J. Anal. Math. 98, 317–348 (2006). https://doi.org/10.1007/BF02790279

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  • DOI: https://doi.org/10.1007/BF02790279

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