Radial and non-radial multiple solutions to a general mixed dispersion NLS equation

Abstract

Abstract We study the following nonlinear Schrödinger equation with a fourth-order dispersion term Δ 2 u − β Δ u = g ( u ) in  R N in the positive and zero mass regimes: in the former, N ⩾ 2 and β > − 2 m , where m > 0 depends on g; in the latter, N ⩾ 3 and β > 0. In either regimes, we find an infinite sequence of solutions under rather generic assumptions about g; if N = 2 in the positive mass case, or N = 4 in the zero mass case, we need to strengthen such assumptions. Our approach is variational.