VARIATIONAL RESULT FOR THE BIFURCATION PROBLEM OF THE HAMILTONIAN SYSTEM

Abstract

We get a theorem which shows the existence of at least four 2�-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory. u p(t) = −λq(t) − Hq(t,p(t),q(t)), u q(t) = λp(t) + Hp(t,p(t),q(t)), where p, q ∈ R n . Let z = (p,q) and J be the standard symplectic structure on R 2n , i.e., J = � 0 −I n In 0 � ,