Prof. Dr. Elmkhan Mahmudov gave a talk as an invited speaker at the II Theoretical and International Scientific Conference on "Theoretical and Application Problems of Mathematics" held between 25-26 April 2023 in Sumqait, and at the International Conference on "Modern Problems of Mathematics and Mechanics" held between 26-28 April 2023 in Baku.

In Sumqait, The paper  Optimal Control of Elliptic Differential Inclusions with Mixed Boundary Conditions deals with the Neumann problem for discrete, discrete-approximate problems and elliptic differential inclusions. Then using the obtained results for discrete inclusions in the form of Euler-Lagrange inclusions necessary and sufficient conditions for optimality are derived for the problems under consideration. Further, these problems are generalized to mixed problems, where the Neumann and Dirichlet conditions are satisfied separately in different parts of the set-valued mapping domain. As an example, a linear optimal control problem is considered, from which the Weierstrass-Pontryagin maximum condition follows. Thus, relying only on the previous auxiliary results, we can obtain the main results of this paper for mixed problems. In turn, the Neumann problem is generalized to the multidimensional case with a second order elliptic operator.

In Baku, the paper Optimization of hyperbolic-type polyhedral differential inclusions concerns the optimization of the Lagrangian problem with differential inclusions (DFI) of hyperbolic type given by polyhedral set-valued mappings. To do this, the corresponding discrete problem with a polyhedral discrete inclusion is defined. Next, using the Farkas theorem, locally conjugate mappings are calculated and necessary and sufficient optimality conditions for polyhedral hyperbolic discrete inclusions are proven. Thus, using only data on the polyhedral nature of the problem, using the discretization method for a hyperbolic type polyhedral discrete-approximate problem the necessary and sufficient conditions of optimality, and then by passing to the limit in the form of the Euler-Lagrange type adjoint DFI, sufficient optimality conditions for a continuous problem are formulated.