Variational stability for generalized ordinary differential equations. (English) Zbl 0574.34034

Schwabik, Štefan

Čas. Pěst. Mat. 109, 389-420 (1984).

Generalized differential equations are studied in the paper from the point of view of stability. The concept of variational stability is used because the solutions of the equations in question are functions of bounded variation on the compact subintervals of the interval of definition. The concept of variational and asymptotic variational stability is completely characterized by a special type of Lyapunov function. The corresponding converse theorems are also derived. Some attention is also paid to the case of stability with respect to perturbations by functions with variations small in a certain sense.

MSC:

34D20	Stability of solutions to ordinary differential equations
34D99	Stability theory for ordinary differential equations

Keywords:

variational stability; Lyapunov function