On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient

Chen, Jianqing

Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 715-736

Abstract (VO)

By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential $$ {\rm i}\varphi _t=-\triangle \varphi +|x|^2\varphi -|x|^b|\varphi |^{p-2}\varphi . $$ We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.

Détail

Classification : 35J20, 35Q55
Keywords: interpolation inequality; inhomogeneous nonlinear Schrödinger equation; harmonic potential; blow-up; global existence; standing waves; strong instability

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