Existence Problems in Second Order Evolution Inclusions: Discretization and Variational Approach

Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

“…Solutions are such that u(•),u(•) andü(•) are Lebesgue integrable andu(•) is AC: we are therefore in a totally different framework than (2.6). Results for this sort of SOSwP can be found in [43] who extend the well-posedness analysis made in [171,170] to similar SOSwP with prox-regular, compact sets S(u), where F (t, u,u) is set-valued, not necessarily bounded. See also [47,66] for similar studies, where S(u) is Lipschitz, closed, prox-regular.…”

General second order functional differential inclusion driven by the sweeping process with subsmooth sets

“…The study of this kind of evolution problems was initiated by Moreau [1] for the Lagrangian system to frictionless unilateral constraints and Castaing [2] when the moving set depends on the state and takes convex compact values. Since then, various generalizations have been obtained, see e.g., [3,4,5,6,7,8,9,10,11] and the references therein. The nonconvex case was considered by [12], the authors proved the existence of solutions to (P) for uniformly prox-regular sets D(t, v(t))) with absolutely continuous variation in space and Lipschitz variation in time and with a single-valued perturbation.…”

Viable Solutions for a Class of Delay Evolution Problems

“…where F is a set-valued function from [0, T ] × C 0 with nonempty convex compact values in E, and φ ∈ C 0 . The existence of viable solutions for such problems with memory has been studied by several authors ( [4], [5], [10], [12], [13], [14]). This class of problems is motivated by the evolution of control systems with feedbacks, dynamic evolutions and planning procedures in microeconomics, for more details and examples, see [1].…”