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Approximate controllability of impulsive semilinear evolution equations in Hilbert spaces
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abstract
Several dynamical systems in fields such as engineering, chemistry, biology, and physics show impulsive behavior by reason of unexpected changes at specific times. These behaviors are described by differential systems under impulse effects. The current paper examines approximate controllability for semi-linear impulsive differential and neutral differential equations in Hilbert spaces. By applying a fixed-point method and semigroup theory, a new sufficient condition is provided for the ($\mathcal{A}$-controllability) approximate controllability of neutral and impulsive differential equations (IDEs). To demonstrate the value of the suggested consequences, three examples are presented, offering improvements over some recent findings.
Forward citations
Cited by 3 Pith papers
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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 b...
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The existence and controllability of nonautonomous system influenced by impulses on both state and control
A fixed point and adjoint resolvent argument is used to claim existence and approximate controllability for nonautonomous impulsive integro-differential systems, with an illustrative heat equation example.
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Remarks on finite-approximate controllability of impulsive evolution systems via resolvent-like operator in Hilbert spaces
The paper extends a known controllability method to impulsive systems, but the main theorem's proof is incomplete.
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