Orbital Stability of Ground States for a Mass Subcritical Fractional Schrodinger-Poisson Equation

Abstract

In this paper, we study the existence of ground state standing waves with prescribed mass constraints for the fractional Schrodinger-Poisson equation \(\mathit{i}\partial_t\psi\) - (- \(\Delta\))\(\\^S\)\(\psi\) - (|\(\mathit{x}\)|\(\\^2\\^t\\^-\\^3\) * |\(\psi\)|\(\\^2\))\(\psi\) + |\(\psi\)|\(\\^p\\^-\\^2\)\(\psi\) = 0, where \(\psi\) : \(\mathbb{R}\\^3\) x \(\mathbb{R}\) \(\to\) \(\mathbb{C}\), s, t \(\in\) (0,1), 2s + 2t > 3 and \(\mathit{p}\) \(\in\) \((2 , {4s \pm 2t \over s+t})\). In particular, in the mass subcritical case but \(p \neq \frac{4 s+2 t}{s+t}\), that is, \(p \in\left(2,2+\frac{4 s}{3}\right) \backslash\left\{\frac{4 s+2 t}{s+t}\right\}\),we prove that the solution with initial datum 0 exists globally and the set of ground states is orbitally stable.