Piecewise Continuous Stepanov-Like Almost Automorphic Functions with Applications to Impulsive Systems
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In this chapter, we discuss Stepanov-like almost automorphic function in the framework of impulsive systems. Next, we establish the existence and uniqueness of such solution of a very general class of delayed model of impulsive neural network. The coefficients and forcing term are assumed to be Stepanov-like almost automorphic in nature. Since the solution is no longer continuous, so we introduce the concept of piecewise continuous Stepanov-like almost automorphic function. We establish some basic and important properties of these functions and then prove composition theorem. Composition theorem is an important result from the application point of view. Further, we use composition result and fixed point theorem to investigate existence, uniqueness and stability of solution of the problem under consideration. Finally, we give a numerical example to illustrate our analytical findings.
KeywordsStepanov-like almost automorphic functions Composition theorem Impulsive differential equations Fixed point method Asymptotic stability
We would like to thank the anonymous referee for his/her constructive comments and suggestions.
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