Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative respect to a left-continuous non-decreasing function replaces classical derivative. The involved set-valued mapping is not assumed have compact and convex values, nor be upper semicontinuous concerning second argument everywhere, as in other related works. A condition involving contingent relative (recently introduced applied initial value problems by R.L. Pouso, I.M. Marquez Albes, J. Rodriguez-Lopez) imposed on set semicontinuity assumption values fail. Based previously obtained results for single-valued cases, existence of solutions proven. It also pointed out that solution uniform convergence topology. In particular, impulsive (with multivalued maps finite or possibly countable moments) without assumptions right-hand side, derived dynamic time scales conditions.