| 概要 | We consider time global behavior of solutions to focusing mass-subcritical NLS equation in framework of weighted $L^2$ space. We prove that there exists an initial data such that (i) corresponding solution does not scatter (non-scattering data); (ii) with respect to a certain scale-invariant quantity, this attains minimum value in all non-scattering data. Here, we call a solution with the above data as a minimal non-scattering solution. In mass-critical and -supercritical cases, it is known that the ground states are this kind of minimal non-scattering solutions. However, in this case, we can show that the non-scattering solution is NOT a standing wave solution such as ground state or excited state. |