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arXiv · 1508.01043

Qualitative properties of solutions for nonlinear Schr\"odinger equations with nonlinear boundary conditions on the half-line

Varga K. Kalantarov·Türker Özsarı
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Abstract

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 Schr\"odinger 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.

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Varga K. Kalantarov, Türker Özsarı. 2015-08-05. Qualitative properties of solutions for nonlinear Schr\"odinger equations with nonlinear boundary conditions on the half-line. https://arxiv.org/abs/1508.01043

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