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On the existence of bounded positive solutions of Schrödinger equations in two-dimensional exterior domains

Hesaaraki, M ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. DOI: 10.1016/j.aml.2007.03.001
  3. Publisher: 2007
  4. Abstract:
  5. We prove under quite general assumptions the existence of a bounded positive solution of the semilinear Schrödinger equation Δ u + f (x, u) = 0 in a two-dimensional exterior domain. Our results are independent of the behavior of f (x, u) when u is sufficiently small or sufficiently large and just require some knowledge about the nonlinearity f (x, u) for a ≤ u ≤ b, for some a, b > 0. We obtain solutions with a prescribed positive lower bound. © 2007 Elsevier Ltd. All rights reserved
  6. Keywords:
  7. Nonlinear equations ; Ordinary differential equations ; Schrodinger equation ; Two dimensional ; Fixed point theory ; Nonlinear ordinary differential equations ; Positive solution ; Subsolution ; Numerical methods
  8. Source: Applied Mathematics Letters ; Volume 20, Issue 12 , December , 2007 , Pages 1227-1231 ; 08939659 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0893965907000808