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Qualitative properties of solutions for nonlinear Schrodinger equations with nonlinear boundary conditions on the half-line

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Özsarı, Türker

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In this paper, we study the interaction between a nonlinear focusing Robin type boundary source, a nonlinear defocusing interior source, and a weak damping term for nonlinear Schrodinger equations posed on the infinite half-line. We construct solutions with negative initial energy satisfying a certain set of conditions which blow-up in finite time in the H-1-sense. We obtain a sufficient condition relating the powers of nonlinearities present in the model which allows construction of blow-up solutions. In addition to the blow-up property, we also discuss the stabilization property and the critical exponent for this model. (C) 2016 AIP Publishing LLC.

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American Institute of Physics (AIP) Publishing

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Mathematical physics

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Journal of Mathematical Physics

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10.1063/1.4941459

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