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ODES RELATED WITH SOME NONLOCAL SCHRÖDINGER EQUATIONS AND ITS APPLICATIONS

  • Received : 2018.02.01
  • Accepted : 2018.10.15
  • Published : 2019.01.31

Abstract

We obtain ordinary differential equations related with some nonlocal Schr$Schr{\ddot{o}}dinger$dinger equations. As applications, we prove finite time blow-up or extinction of solutions.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. R. Carles and C. Gallo, Finite time extinction by nonlinear damping for the Schrodinger equation, Comm. Partial Differential Equations 36 (2011), no. 6, 961-975. https://doi.org/10.1080/03605302.2010.531074
  2. H. Huh, Solution formulas for some nonlocal heat equations, Commun. Korean Math. Soc. 31 (2016), no. 3, 567-573. https://doi.org/10.4134/CKMS.c150197
  3. K. Nakamura and T. Ozawa, Finite charge solutions to cubic Schrodinger equations with a nonlocal nonlinearity in one space dimension, Discrete Contin. Dyn. Syst. 33 (2013), no. 2, 789-801. https://doi.org/10.3934/dcds.2013.33.789