Abstract
This article is concerned with time global behavior of solutionsto focusing mass-subcritical nonlinear Schrödinger equation of power type withdata in a critical homogeneous weighted $L^2$ space. We givea sharp sufficient condition for scattering by proving existence ofa threshold solution which does not scatter at least forone time direction and of which initial data attains minimumvalue of a norm of the weighted $L^2$ space inall initial value of non-scattering solution. Unlike in the mass-criticalor -supercritical case, ground state is not a threshold. Thisis an extension of previous author's result to the casewhere the exponent of nonlinearity is below so-called Strauss number.A main new ingredient is a stability estimate in aLorenz-modified-Bezov type spacetime norm.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
