Mass-subcritical Half-Wave Equation with mixed nonlinearities: existence and non-existence of ground states

2025/04/10 by Bellazzini, Jacopo, Forcella, Luigi · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2504.07488

Abstract

We consider the problem of existence of constrained minimizers for the focusing mass-subcritical Half-Wave equation with a defocusing mass-subcritical perturbation. We show the existence of a critical mass such that minimizers do exist for any mass larger than or equal to the critical one, and do not exist below it. At the dynamical level, in the one dimensional case, we show that the ground states are orbitally stable.

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• NLS with mass-subcritical combined nonlinearities: small mass L²-scattering

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