Second Order Nonlinear Evolution Inclusions II: Structure of the Solution Set

We continue the work initiated in [1] (Second order nonlinear evolution inclusions I: Existence and relaxation results. Acta Mathematics Science, English Series, 21(5), 977-966 (2005)) and study the structural properties of the solution set of second order evolution inclusions which are defined in the analytic framework of the evolution triple. For the convex problem we show that the solution set is compact R , while for the nonconvex problem we show that it is path connected. Also we show that the solution set is closed only if the multivalued nonlinearity is convex valued. Finally we illustrate the results by considering a nonlinear hyperbolic problem with discontinuities.