## Czesław Olech, professor

* Ph. D.: IM PAN 1958, habilitation: IM PAN 1962*

Main fields of research interest: ordinary differential equations and
mathematical theory of optimal control.

Contributions to O.D.E.: various applications of Wa/zewski topological method
in studying asymptotic behaviour of solutions,
exact estimates of exponential
growth of solution of linear second order differential equations with bounded
coefficients,
theorems concerning global asymptotic stability of the
autonomous system on the plane with stable Jacobian matrix at each point of
the plane,
results establishing relation between question of global asymptotic stability
of an autonomous system and that of global
one-to-oneness of a differentiable map,
contribution to the question
whether unicity condition implies convergence of succesive approximation to
solutions of ordinary differential equations.

Contribution to control theory: estabilishing a most general version of the
so-called bang-bang principle for linear control problem by detailed study
of the integral of set valued map,
existence theorems for
optimal control problem with unbounded controls and multidimensional cost
functions,
existence of solution of differential inclusions with nonconvex
right-hand side, characterization of controllability of convex processes.

Doctor Honoris Causa AGH University of Science and Technology