THE MINIMAL PERIOD PROBLEM OF PERIODIC-SOLUTIONS FOR AUTONOMOUS SUPERQUADRATIC 2ND-ORDER HAMILTONIAN-SYSTEMS

In this paper, we study the existence of periodic solutions with prescribed minimal period for superquadratic autonomous second order Hamiltonian systems defined on R(n) with no convexity assumptions. We use the direct variational approach for this problem on a W1,2-space of even functions, and prove new iteration inequalities on Morse indices. Using these tools and the saddle point theorem, we obtain results under precisely Rabinowitz' superquadratic condition on potential functions. We show that for every T>0 the above mentioned system possesses a T-periodic even solution with minimal period not smaller than T/(n+2). (C) 1994 Academic Press, Inc.