Scattering for the focusing energy-subcritical NLS

Details Scattering for the focusing energy-subcritical NLS Scattering for the focusing energy-subcritical NLS

2011-01-16

arxiv.org/abs/1101.3058v1

Mathematics

Analysis of PDEs

30 pages

Scientific paper

For the 3D focusing cubic nonlinear Schrodinger equation, Scattering of $H^1$ solutions inside the (scale invariant) potential well was established by Holmer and Roudenko~\cite{HR2} (radial case) and Duyckaerts, Holmer and Roudenko~\cite{DHR} (general case). In this paper, we extend this result to arbitrary space dimensions and focusing, mass-supercritical and energy-subcritical power nonlinearities, by adapting the method of~\cite{DHR}.

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