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Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

Stamov, G. — 1996

Serdica Mathematical Journal

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

Stamov, G. — 1995

Serdica Mathematical Journal

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7. Sufficient conditions are obtained for the existence of local integral manifolds of autonomous systems of differential equations with impulses at fixed moments. In case of perturbations of the nonlinear part an estimate of the difference between the manifolds is obtained.

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