Approximate controllability is established for semilinear impulsive neutral integro-differential equations with fading memory in reflexive Banach spaces, under a linear controllability condition and a strong uniform boundedness condition on the nonlinearity.
Remarks on finite-approximate controllability of impulsive evolution systems via resolvent-like operator in Hilbert spaces
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abstract
In this manuscript, we examine impulsive evolution systems in Hilbert spaces. Using a resolvent-like operator, we first establish the finite-approximate controllability for linear systems. Subsequently, by applying the Schauder fixed-point theorem (SFPT), we prove the existence of a solution and demonstrate the finite-approximate controllability of semilinear impulsive systems in Hilbert spaces. Finally, we extend these results to a broader application, specifically to the heat equation.
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Study on Control Problem of a Impulsive Neutral Integro-Differential Equations with Fading Memory
Approximate controllability is established for semilinear impulsive neutral integro-differential equations with fading memory in reflexive Banach spaces, under a linear controllability condition and a strong uniform boundedness condition on the nonlinearity.