Abstract
Necessary and sufficient conditions are found for existence of at least one bounded nonoscillatory solution of a class of impulsive differential equations of third order and fixed moments of impulse effect. Some asymptotic properties of the nonoscillating solutions are investigated.
Highlights
The impulsive differential equations with deviating argument are adequate mathematical models of numerous processes and phenomena in physics, biology and electrical engineering
Necessary and sufficient conditions are found for existence of at least one bounded nonoscillatory solution of a class of impulsive differential equations of third order and fixed moments of impulse effect
In spite of wide possibilities for their application, the theory of these equations is developing rather slowly because of considerable difficulties in technical and theoretical character related to their study
Summary
The impulsive differential equations with deviating argument are adequate mathematical models of numerous processes and phenomena in physics, biology and electrical engineering. Necessary and sufficient conditions are found for existence of at least one bounded nonoscillatory solution of a class of impulsive differential equations of third order and fixed moments of impulse effect. In the recent twenty years, the number of investigations devoted to the oscillatory and nonoscillatory behavior of the solutions of functional differential equations has considerably increased.
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