Approximate controllability of second order impulsive systems with state-dependent delay in Banach spaces
Soniya Singh, Sumit Arora, Manil T. Mohan, Jaydev Dabas
Abstract
<p style='text-indent:20px;'>In this paper, we consider the second order semilinear impulsive differential equations with state-dependent delay. First, we consider a linear second order system and establish the approximate controllability result by using a feedback control. Then, we obtain sufficient conditions for the approximate controllability of the considered system in a separable, reflexive Banach space via properties of the resolvent operator and Schauder's fixed point theorem. Finally, we apply our results to investigate the approximate controllability of the impulsive wave equation with state-dependent delay.</p>
Topics & Concepts
ControllabilityBanach spaceMathematicsResolventBanach fixed-point theoremOrder (exchange)Pure mathematicsC0-semigroupApplied mathematicsSeparable spaceFixed-point theoremMathematical analysisState (computer science)Operator (biology)UniquenessFinanceGeneRepressorEconomicsChemistryAlgorithmBiochemistryTranscription factorStability and Controllability of Differential EquationsNonlinear Differential Equations AnalysisAdvanced Mathematical Modeling in Engineering