On a system of Schrödinger equations with general quadratic-type nonlinearities
Fecha
2021-07-27
Tipo
artículo original
Autores
Noguera Salgado, Norman F.
Pastor Ferreira, Ademir
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Resumen
In this work, we study a system of Schrödinger 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 of 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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Palabras clave
global well-posedness, Nonlinear Schrödinger equations, blow-up, ground states, nonlinear stability