Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part

We present an abstract critical point theorem about the existence of infinitely many critical orbits to strongly indefinite functionals with a sign-changing nonlinear part defined on a dislocation space with a discrete group action. We apply the abstract result to a Schrödinger equation (Formula presented.) with 0 in the spectral gap of the Schrödinger operator -Δ+V(x), that appears in nonlinear optics. We also consider equations with singular potentials arising from the study of cylindrically symmetric, electromagnetic waves to the system of Maxwell equations.