Optimal Control of an Evolution Problem Involving Time-Dependent Maximal Monotone Operators

Journal of Optimization Theory and Applications - We consider a control problem in a finite-dimensional setting, which consists in finding a minimizer for a standard functional defined by way of...     

A Delay Second-Order Set-Valued Differential Equation with Hukuhara Derivatives

In this article, we study a second-order differential equation with three-point boundary conditions with the notion of Hukuhara derivatives. The existence and uniqueness of a solution is given under a Lipschitz condition on the right-hand side in the second and third variables.     

Perturbed Evolution Problems with Continuous Bounded Variation in Time and Applications

This paper is devoted to the study of evolution problems of the form \(-\frac {du}{dr}(t) \in A(t)u(t) + f(t, u(t))\) in a new setting, where, for each t, A(t) : D(A(t)) → 2 ^H is a maximal monotone operator in a Hilbert space H and the mapping t?A(t) has continuous bounded or Lipschitz variation on [0, T], in the sense of Vladimirov’s pseudo-distance. The measure dr gives an upper bound of that variation. The perturbation f is separately integrable on [0, T] and separately Lipschitz on H. Several versions and new applications are presented.     

Mixed Semicontinuous Perturbation of Nonconvex State-Dependent Sweeping Process

In this paper we prove a result on the existence of solutions of a first-order differential inclusion governed by a class of nonconvex sweeping process. The moving set involved in the process is prox-regular and depends both on the time and on the state.