A note on Berestycki-Cazenave's classical instability result for nonlinear Schrödinger equations

Stefan Le Coz (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

In this note we give an alternative, shorter proof of the classical result of Berestycki and Cazenave on the instability by blow-up for the standing waves of some nonlinear Schrödinger equations.

Mots clés: nonlinear Schrödinger equations; standing waves; instability; blow-up; variational methods

Domaines: Equations aux dérivées partielles [math.AP]

Stefan Le Coz. A note on Berestycki-Cazenave's classical instability result for nonlinear Schrödinger equations. Advanced Nonlinear Studies, 2008, pp.Adv. Nonlinear Stud. 8 (2008), no. 3, 455-463. ⟨hal-00182752⟩