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Nonexistence of global solutions of nonlinear Schrodinger equations in non star-shaped domains

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  • In this paper, we discuss the nonexistence of global solutions of mixed problems of the nonlinear Schödinger equations with power nonlinearity. When the domain is whole space, there are many results concerning the nonexistence of global solutions ( or existence of blow-up solutions ) for the equation. For the case of a general domain, there are few studies of blowing-up conditions. The main purpose of this paper is to discuss the nonexistence of global solutions in a deformed tube-shaped domain which is not star-shaped.
    Mathematics Subject Classification: Primary: 35B30, 35Q55; Secondary: 81Q99.


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