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A Note on the Inhomogeneous Schrödinger Equation with Mixed Power Nonlinearity

Commun. Math. Anal.
Volume 18, Number 2 (2015), 34 - 53

A Note on the Inhomogeneous Schrödinger Equation with Mixed Power Nonlinearity

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Abstract

We investigate the initial value problem for an inhomogeneous nonlinear Schrödinger equation with a combined power nonlinearity. We prove global well-posedness in the defocusing case. In the focusing case, we prove existence of ground state and nonlinear instability of standing waves.