  We study the following nonlinear Schr\"odinger equation $$-\Delta u + V(x) u
= g(x,u),$$ where V and g are periodic in x. We assume that 0 is a right
boundary point of the essential spectrum of $-\Delta+V$. The superlinear and
subcritical term g satisfies a Nehari type monotonicity condition. We employ a
Nehari manifold type technique in a strongly indefitnite setting and obtain the
existence of a ground state solution. Moreover we get infinitely many
geometrically distinct solutions provided that g is odd.
