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On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue

Author

Listed:
  • Scipio Cuccagna

    (Department of Mathematics, Informatics and Geosciences, University of Trieste, Via Valerio 12/1, 34127 Trieste, Italy)

  • Masaya Maeda

    (Department of Mathematics and Informatics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan)

Abstract

We prove in dimension d = 1 a result similar to a classical paper by Soffer and Weinstein, Jour. Diff. Eq. 98 (1992), improving it by encompassing for pure power nonlinearities the whole range of exponents p > 1 . The proof is based on the virial inequality of Kowalczyk et al., J. Eur. Math. Soc. (JEMS) 24 (2022), with smoothing estimates as shown in Mizumachi J. Math. Kyoto Univ. 48 (2008).

Suggested Citation

  • Scipio Cuccagna & Masaya Maeda, 2024. "On Small Energy Solutions of the Nonlinear Schrödinger Equation in 1D with a Generic Trapping Potential with a Single Eigenvalue," Mathematics, MDPI, vol. 12(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3876-:d:1540070
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