Abstract
In this paper we consider a second order multivalued periodic boundary value problem with a nonconvex and unbounded orientor field (set-valued vector field). Using a directionally continuous selector, through its Filippov regularization we produce a convex-valued, bounded multifunction and with this as orientor field we introduce a new multivalued periodic problem. Using the Leray-Schauder principle, we solve the convex problem and then we show that its solutions also solve the original nonconvex problem.
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