Existence of blowing-up solutions to some Schrödinger equations including nonlinear amplification with small initial data
DOI:
https://doi.org/10.5564/jasea.v2i1.3340Keywords:
Nonlinear Schroedinger equation, nonliner amplification, blowing-up solution, small initial dataAbstract
We consider the existence of blowing-up solutions to some Schroedinger equations including nonlinear amplification. The blow-up is considered in L2(R). Even though initial data are taken so small, there exist some solutions blowing-up in finite time. The theorem in this paper is an extension of Cazenave-Martel-Zhao’s result [7] from the point of making the lower bound of power of nonlinearity extended and from the point of ensuring that blowing-up solutions exist even for small initial data.
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