Browsing by Author "Bainov D."
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Item Asymptotic properties of solutions of a class of impulsive differential equations of second order with a retarded argument(1997-01-01) Bainov D.; Dimitrova M.; Dishliev A.Some asymptotic properties are studied for the solutions of a class of impulsive differential equations of second order with retarded argument and fixed moments of impulse effect. Sufficient conditions are found for oscillation of all bounded solutions. © 1997, Department of Mathematics, Tokyo Institute of Technology. All rights reserved.Item Asymptotic properties of solutions of a class of impulsive differential equations of second order with a retarded argument(1997-01-01) Bainov D.; Dimitrova M.; Dishliev A.Some asymptotic properties are studied for the solutions of a class of impulsive differential equations of second order with retarded argument and fixed moments of impulse effect. Sufficient conditions are found for oscillation of all bounded solutions. © 1997, Department of Mathematics, Tokyo Institute of Technology. All rights reserved.Item Continuous dependence of the solution of a system of differential equations with impulses on the impulse hypersurfaces(1988-11-01) Dishliev A.; Bainov D.In the present paper the initial value problem is considered for systems of ordinary differential equations with impulses where the impulses are realized in the moments when the integral curve of the system meets some of previously given hypersurfaces called impulse hypersurfaces. Sufficient conditions for the continuous dependence of the solution on the impulse hypersurfaces are found. © 1988.Item Continuous dependence of the solution of a system of differential equations with impulses on the impulse hypersurfaces(1988-11-01) Dishliev A.; Bainov D.In the present paper the initial value problem is considered for systems of ordinary differential equations with impulses where the impulses are realized in the moments when the integral curve of the system meets some of previously given hypersurfaces called impulse hypersurfaces. Sufficient conditions for the continuous dependence of the solution on the impulse hypersurfaces are found. © 1988.Item Continuous Dependence on the Initial Condition of the Solution of a System of Differential Equations with Variable Structure and with Impulses(1987-01-01) Dishliev A.; Bainov D.Item Continuous Dependence on the Initial Condition of the Solution of a System of Differential Equations with Variable Structure and with Impulses(1987-01-01) Dishliev A.; Bainov D.Item Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations(1996-06-28) Bainov D.; Dishliev A.; Stamova I.In the present paper, by means of a suitable comparison lemma sufficient conditions for uniform Lipschitz stability of an arbitrary solution of an impulsive system of differential-difference equations with variable impulsive perturbations are obtained.Item Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations(1996-06-28) Bainov D.; Dishliev A.; Stamova I.In the present paper, by means of a suitable comparison lemma sufficient conditions for uniform Lipschitz stability of an arbitrary solution of an impulsive system of differential-difference equations with variable impulsive perturbations are obtained.Item Oscillation of the solutions of a class of impulsive differential equations with a deviating argument(1998-01-01) Bainov D.; Dimitrova M.; Dishliev A.Sufficient conditions are found for oscillation of all solutions of a class of impulsive differential equations with deviating argument. ©1998 by North Atlantic Science Publishing Company.Item Oscillation of the solutions of a class of impulsive differential equations with a deviating argument(1998-01-01) Bainov D.; Dimitrova M.; Dishliev A.Sufficient conditions are found for oscillation of all solutions of a class of impulsive differential equations with deviating argument. ©1998 by North Atlantic Science Publishing Company.Item Oscillation of the solutions of impulsive differential equations and inequalities with a retarded argument(1998-01-01) Bainov D.; Dimitrova M.; Dishliev A.Sufficient conditions for oscillation of all solutions of a class of impulsive differential equations and inequalities with a retarded argument and fixed moments of impulse effect are found. © 1998 Rocky Mountain Journal of Mathematics. © 1998 Applied Probability Trust.Item Oscillation of the solutions of impulsive differential equations and inequalities with a retarded argument(1998-01-01) Bainov D.; Dimitrova M.; Dishliev A.Sufficient conditions for oscillation of all solutions of a class of impulsive differential equations and inequalities with a retarded argument and fixed moments of impulse effect are found. © 1998 Rocky Mountain Journal of Mathematics. © 1998 Applied Probability Trust.Item Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population(1990-01-01) Bainov D.; Dishliev A.The dynamics of a population whose mathematical model is the equation of Verhulst is considered. From the population, by discrete external effects (in the form of impulses), a certain quantity of biomass is taken away (or added). This process is described by means of differential equations with impulses at fixed moments. The moments and the magnitudes of the impulses are determined so that the time of regeneration of the quantity of biomass taken away from the population be minimal. © 1990.Item Uniform Stability with Respect to the Impulse Hypersurfaces of the Solutions of Differential Equations with Impulses(1993-01-05) Bainov D.; Dishliev A.The systems of differential equations with impulses are divided into several classes according to the way in which the moments of the impulses are determined. In the present paper the initial value problem is considered for systems of differential equations for which the impulses are realized at the moments when the integral curve of the problem meets certain hypersurfaces, called impulse hypersurfaces, of the extended phase space. The notions of strong uniform stability of the solutions of systems without impulses and uniform stability with respect to the impulse hypersurfaces of the solutions of systems with impulses are introduced. The main results are given in two theorems. The first one contains sufficient conditions under which strong uniform stability of the zero solution of the respective system without impulses implies uniform stability with respect to the impulse hypersurfaces of the zero solution of the initial system with impulses. In the second theorem sufficient conditions are given under which uniform Lipschitz stability of the zero solution of the corresponding system without impulses implies uniform stability with respect to the impulse hypersurfaces of the zero solution of the initial system with impulses. © 1993 Academic Press, Inc.Item Uniform Stability with Respect to the Impulse Hypersurfaces of the Solutions of Differential Equations with Impulses(1993-01-05) Bainov D.; Dishliev A.The systems of differential equations with impulses are divided into several classes according to the way in which the moments of the impulses are determined. In the present paper the initial value problem is considered for systems of differential equations for which the impulses are realized at the moments when the integral curve of the problem meets certain hypersurfaces, called impulse hypersurfaces, of the extended phase space. The notions of strong uniform stability of the solutions of systems without impulses and uniform stability with respect to the impulse hypersurfaces of the solutions of systems with impulses are introduced. The main results are given in two theorems. The first one contains sufficient conditions under which strong uniform stability of the zero solution of the respective system without impulses implies uniform stability with respect to the impulse hypersurfaces of the zero solution of the initial system with impulses. In the second theorem sufficient conditions are given under which uniform Lipschitz stability of the zero solution of the corresponding system without impulses implies uniform stability with respect to the impulse hypersurfaces of the zero solution of the initial system with impulses. © 1993 Academic Press, Inc.