An inhomogeneous nonlinear Schrödinger equation is considered, which is invariant under -scaling. The sharp condition for global existence of -solutions is established, involving the-norm of the ground state of the stationary equation. Strong instability of standing waves is proved by constructing self-similar solutions blowing up in finite time.
Cite this article
François Genoud, An Inhomogeneous, -Critical, Nonlinear Schrödinger Equation. Z. Anal. Anwend. 31 (2012), no. 3, pp. 283–290DOI 10.4171/ZAA/1460