Existence and multiplicity of nonzero periodic solution with saddle point character for some nonautonomous second order systems ✩

The purpose of this paper is to study the existence and multiplicity of nonzero periodic solutions with saddle point character for the following nonautonomous second order systems: ¨u(t)=∇F(t, u(t)), a.e. t ∈ [0,T ], u(0) − u(T )= ˙u(0)− ˙u(T ) = 0. Some new existence and multiplicity theorems are obtained by using saddle point reduction method and a three-critical-point theorem proposed by Brezis and Nirenberg.  2004 Elsevier Inc. All rights reserved.