Kogut O.P.

Solutions properties for one class of parameterized operator inclusions

This paper provides the insights into the properties of solutions for parameterized operator inclusions with multi-valued maps of type. We prove the resolvability of such inclusions, weak compactness and parameter dependence of their solution. Moreover, we provide the example, illustrating the obtained results.

The sufficient conditions of the shape stability for perturbation of the one class of optimal control problems

We address the optimal control problems in the coefficients for a nonlinear elliptic equation with Dirichlet boundary conditions for generalized solenoidal controls. We define the shape stability concept for optimal control problems. Finally, we reveal the sufficient conditions for perturbation of the domain, under which the shape stability of the problem under study occurs.