E. K. Makarov
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.