On nonlinear Schrödinger equations with attractive inverse-power potentials

Van Duong Dinh

Abstract


We study the Cauchy problem for nonlinear Schrödinger equations with attractive inverse-power potentials. By using variational arguments, we first determine a sharp threshold of global well-posedness and blow-up for the equation in the mass-supercritical case. We next study the existence and orbital stability of standing waves for the problem in the mass-subcritical and mass-critical cases. In the mass-critical case, we give a detailed description of the blow-up behavior of standing waves when the mass tends to a critical value.

Keywords


Nonlinear Schrödinger equation; inverse-power potential; standing waves; stability; global well-posedness; blow-up

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