Orbital stability of standing waves for Schrödinger type equations with slowly decaying linear potential

Abstract

In this paper, kinds of Schrödinger type equations with slowly decaying linear potential and power type or convolution type nonlinearities are considered. By using the concentration compactness principle, the sharp Gagliardo–Nirenberg inequality and a refined estimate of the linear operator, the existence and orbital stability of standing waves in L2-subcritical and L2-critical cases are established in a systematic way.