Abstract. In this paper we study a quasilinear second order ordinary differential equation with periodic boundary conditions and a discontinuous vector field. We pass to a multivalued problem by filling in the gaps at the discontinuity points. Then, for the multivalued problem we prove the existence of a solution using techniques from the nonsmooth critical point theory.

AMS Subject Classification (1991): 34C25

Keyword(s): Nonsmooth critical point theory, locally Lipschitz functional, generalized subdifferential, saddle point theorem, eigenvalue, nonresonance condition, Palais-Smale condition, Poincaré-Wirtinger inequality

Received September 9, 1997, and in revised form January 25, 1999. (Registered under 2700/2009.)