| Popis: |
This paper is a sequel to the paper (Hamano and Ikeda, Proc. Amer. Math. Soc. To appear). In this paper, we consider the nonlinear Schrodinger equation with a real-valued linear potential and p-th order gauge invariant nonlinearity. Our aim of this paper is to characterize the ground state of the elliptic equation corresponding to the time-dependent problem by the virial functional (see Definition 1.2). In order to study the ground state, we consider attainability of a minimization problem about the elliptic equation. As its application, we give a sufficient condition on the initial data, under which the energy solution can be extended globally in time. We note that the condition is defined by the minimum value of the minimization problem. |
