Periodic solutions of superlinear impulsive differential equations: A geometric approach

A geometric method is introduced to study superlinear second order differential equations with impulsive effects. Basing on a reference continuous polar lifting of a planar orientation-preserving homeomorphism, we prove via the Poincaré–Birkhoff twist theorem the existence of infinitely many periodic solutions of conservative superlinear second order equations with the finite twist impulsive terms. We also prove, by developing a new twist fixed point theorem, the existence of periodic solutions for non-conservative superlinear second order equations with degenerate impulsive terms.