Multiple Periodic Solutions for a Class of Nonlinear Nonautonomous Wave Equations.

In this paper. by means of our Z, index theory developed recently we study the existence of multiple periodic solutions for asymptotically linear nonautonomous wave equations .All previous known re sults rely either on the oddness of nonlinear terms.or on autonomous systems, and the best result for the gen eral case is the existence of two nontrivial periodic solutions (Amann. Zehnder. K.C.Chang.S.P. Wu. S.J.Li.Z.Q. Wang). In this paper. under the assumption that the nonlinear term is T/p periodic we discuss multiple periodic solutions of nonautonomous systems and generalize a series of previous results.