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.)
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