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arXiv · 1908.04159

On a system of Schr\"odinger equations with general quadratic-type nonlinearities

Norman Noguera·Ademir Pastor
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Abstract

In this work we study a system of Schr\"odinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in terms on the ground state solutions associated with the corresponding elliptic system, which in turn are obtained by applying variational methods. By using the concentration-compactness method we also investigate the nonlinear stability/instability of the ground states.

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Norman Noguera, Ademir Pastor. 2019-08-12. On a system of Schr\"odinger equations with general quadratic-type nonlinearities. https://arxiv.org/abs/1908.04159

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