We derive partial diierential inclusions of hyperbolic type solutions of which are feedbacks governing viable (controlled invariant) solutions of a control system. We also show that the tracking property leads to such partial diierential inclusions. We state a variational principle and an existence theorem of a (single-valued contingent) solution to such an inclusion.

We introduce and study a new class of generalized nonlinear implicit quasivariational inclusions involving relaxed Lipschitzian mappings. We prove the existence of solution for the generalized nonlinear implicit quasivariational inclusions and construct some new stable perturbed iterative algorithms with errors. We also give an application to a class of generalized nonlinear implicit variationa...

This paper studies a general optimal control problem for nonconvex delay-differential inclusions with endpoint constraints. In contrast to previous publications on this topic, we incorporate time-dependent set constraints on the initial interval, which are specific for systems with delays and provide an additional source for optimization. Our variational analysis is based on well-posed discrete...

We present projection-iterative schemes for the realization of variational-grid (finite-element and local-variation) methods aimed at solution various variational problems mechanics elastic elastoplastic solids with inclusions holes. By using solutions deformation inhomogeneous isotropic plates cylindrical shells holes kinds as examples, we analyze mutual influence inclusions. investigate probl...

Sensitivity analysis for relaxed cocoercive variational inclusions based on the generalized resolvent operator technique is discussed The obtained results are general in nature.

We introduce and study a new class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases. By applying the resolvent operator technique and fixed point theorem, we suggest a new perturbed three-step iterative algorithm with errors for solving the class of variational inequalities. Several exi...

In this paper, we prove the existence of solutions for a class of nonlinear variational inclusion problems in semi-inner product spaces. We construct an iterative algorithm for approximating the solution for the class of variational inclusions involving A-monotone operators by using the resolvent operator technique.