Zhivko S Athanassov - Academia.edu (original) (raw)
Uploads
Papers by Zhivko S Athanassov
Glasgow Mathematical Journal, 1985
In this paper we study the asymptotic behaviour of the following systems of ordinary differential... more In this paper we study the asymptotic behaviour of the following systems of ordinary differential equations:where the identically zero function is a solution of (N) i.e. f(t, 0)=0 for all time t. Suppose one knows that all the solutions of (N) which start near zero remain near zero for all future time or even that they approach zero as time increases. For the perturbed systems (P) and (P1) the above property concerning the solutions near zero may or may not remain true. A more precise formulation of this problem is as follows: if zero is stable or asymptotically stable for (N), and if the functions g(t, x) and h(t, x) are small in some sense, give conditions on f(t, x) so that zero is (eventually) stable or asymptotically stable for (P) and (P1).
Applicable Analysis, 1986
We prove that three of the most often used definitions of the positive definiteness of Liapunov f... more We prove that three of the most often used definitions of the positive definiteness of Liapunov functions in the theory of stability are equivalent.
Journal of Mathematical Analysis and Applications, 1982
Glasgow Mathematical Journal, 1985
In this paper we study the asymptotic behaviour of the following systems of ordinary differential... more In this paper we study the asymptotic behaviour of the following systems of ordinary differential equations:where the identically zero function is a solution of (N) i.e. f(t, 0)=0 for all time t. Suppose one knows that all the solutions of (N) which start near zero remain near zero for all future time or even that they approach zero as time increases. For the perturbed systems (P) and (P1) the above property concerning the solutions near zero may or may not remain true. A more precise formulation of this problem is as follows: if zero is stable or asymptotically stable for (N), and if the functions g(t, x) and h(t, x) are small in some sense, give conditions on f(t, x) so that zero is (eventually) stable or asymptotically stable for (P) and (P1).
Applicable Analysis, 1986
We prove that three of the most often used definitions of the positive definiteness of Liapunov f... more We prove that three of the most often used definitions of the positive definiteness of Liapunov functions in the theory of stability are equivalent.
Journal of Mathematical Analysis and Applications, 1982