Bifurcation into spectral gaps for strongly indefinite Choquard equations

Abstract

In this paper, we consider the semilinear elliptic equations [Formula: see text] where [Formula: see text] is a Riesz potential, [Formula: see text], [Formula: see text] and [Formula: see text] is continuous periodic. We assume that [Formula: see text] lies in the spectral gap [Formula: see text] of [Formula: see text]. We prove the existence of infinitely many geometrically distinct solutions in [Formula: see text] for each [Formula: see text], which bifurcate from [Formula: see text] if [Formula: see text]. Moreover, [Formula: see text] is the unique gap-bifurcation point (from zero) in [Formula: see text]. When [Formula: see text], we find infinitely many geometrically distinct solutions in [Formula: see text]. Final remarks are given about the eventual occurrence of a bifurcation from infinity in [Formula: see text].