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March/April 2019 Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity
Satoshi Masaki, Hayato Miyazaki
Differential Integral Equations 32(3/4): 121-138 (March/April 2019).

Abstract

We consider large time behavior of solutions to the nonlinear Schrödinger equation with a homogeneous nonlinearity of the critical order which is not necessarily a polynomial. We treat the case in which the nonlinearity contains non-oscillating factor $|u|^{1+2/d}$. The case is excluded in our previous studies. It turns out that there are no solutions that behave like a free solution with or without logarithmic phase corrections. We also prove nonexistence of an asymptotic free solution in the case that the gauge invariant nonlinearity is dominant, and give a finite time blow-up result.

Citation

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Satoshi Masaki. Hayato Miyazaki. "Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity." Differential Integral Equations 32 (3/4) 121 - 138, March/April 2019.

Information

Published: March/April 2019
First available in Project Euclid: 23 January 2019

zbMATH: 07036978
MathSciNet: MR3909981

Subjects:
Primary: 35B44 , 35P25 , 35Q55

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 3/4 • March/April 2019
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