PERIODIC SOLUTIONS OF SUPERLINEAR PLANAR HAMILTONIAN SYSTEMS WITH INDEFINITE TERMS

Existence of infinitely many periodic solutions for a planar Hamil-tonian system Jz ' = backward difference zH(t, z) is proved. We investigate the case in which backward difference zH(t, z) satisfies a general superlinear condition at infinity via rotation numbers and x partial differential partial differential x H(t, x, y) is an indefinite term. Our approach is based on the Poincare-Birkhoff theorem and the spiral property of large amplitude solutions. Our results generalize the classical result in Jacobowitz [13] and Hartman [12] for second order scalar equations.