In this paper, we employ the well-known Krasnoselskii fixed point theorem to study the existence and n-multiplicity of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensi...

Abstract It has become imperative in recent times to determine the properties of the solutions of certain mathematical equations or inequalities from the knowledge of associated inequalities or equations. In this paper, a number of oscillatory properties of the solutions of impulsive differential inequalities are established using the knowledge of those of their associated equations and what is...

We obtain necessary conditions of optimality for impulsive Volterra integral equations with switching and impulsive controls, with variable impulse time-instants. The present work continues and complements our previous work on impulsive Volterra control with fixed impulse times.

*Correspondence: [email protected] 1School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, P.R. China Full list of author information is available at the end of the article Abstract In this paper, some new generalized retarded inequalities for discontinuous functions are discussed, which are effective in dealing with the qualitative theory of some impulsive differential ...

Impulsive differential equations play a very important role in understanding mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology, economics and so on, see [1,2,8,10,17]. About wide applications of the theory of impulsive differential equations to different areas, we refer the readers to monographs [5,7,18,19] and the re...

In this paper, we study the existence of extremal solutions forimpulsive delay fuzzy integrodifferential equations in$n$-dimensional fuzzy vector space, by using monotone method. Weshow that obtained result is an extension of the result ofRodr'{i}guez-L'{o}pez cite{rod2} to impulsive delay fuzzyintegrodifferential equations in $n$-dimensional fuzzy vector space.