On solitary wave solutions to dispersive equations with double power nonlinearities

We study semilinear elliptic equations with the fractional Laplacian in $\mathbb{R}$. The equations with single power nonlinearities have been observed by Weinstein(1987), Frank–Lenzmann(2013) and so on. We focus on the equations with double power nonlinearities and consider the existence of ground states.