E. K. Makarov

Vector Optimization Tools in Asymptotic Theory of Total Differential Equations

abstract:
We apply the basic concepts of vector optimization theory to certain problems arising in the asymptotic theory of total differential equations. This approach enables us to establish  interrelations between characteristic functionals and characteristic exponents, which are the main asymptotic characteristics of solutions of these equations. We are also enabled to construct a set of proper characteristic functionals with a number of useful properties. Using these results, we study the structure of characteristic sets, the properties of weakly regular linear total differential equations, and the behavior of characteristic functionals of equations under exponentially decreasing perturbations.

Mathematics Subject Classification: 34G10, 34D08, 90C29.

Key words and phrases: Total differential equation, characteristic exponent, characteristic functional, proper efficiency.