On solitary wave solutions to dispersive equations with double power nonlinearities

Abstract

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.

20 page. Abstract is corrected

References in corpus (1)

• The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications