Zhivko S Athanassov - Profile on Academia.edu (original) (raw)

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Papers by Zhivko S Athanassov

Research paper thumbnail of On the asymptotic behaviour of nonlinear systems of ordinary differential equations

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).

Research paper thumbnail of Positive definite functions in stability theory

Positive definite functions in stability theory

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.

Research paper thumbnail of Perturbation theorems for nonlinear systems of ordinary differential equations

Perturbation theorems for nonlinear systems of ordinary differential equations

Journal of Mathematical Analysis and Applications, 1982

Research paper thumbnail of On the asymptotic behaviour of nonlinear systems of ordinary differential equations

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).

Research paper thumbnail of Positive definite functions in stability theory

Positive definite functions in stability theory

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.

Research paper thumbnail of Perturbation theorems for nonlinear systems of ordinary differential equations

Perturbation theorems for nonlinear systems of ordinary differential equations

Journal of Mathematical Analysis and Applications, 1982

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