<p>This paper investigates the problem of approximate controllability for a class of Sobolev type second order impulsive differential inclusions governed by hemivariational inequalities in Hilbert spaces. The considered system incorporates both impulsive effects and nonsmooth dynamics arising from the Clarke subdifferential framework. By employing the theory of cosine operator families, multivalued analysis, and fixed point techniques, we establish sufficient conditions for the existence of mild solutions and derive approximate controllability conditions. Furthermore, we demonstrate the impulses and hemivariational inequalities influence the controllability behavior of the system. Finally, a theoretical example is provided to illustrate the applicability of the developed controllability results.</p>

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Discussion on the Approximate Controllability Results for Sobolev Type Second Order Impulsive Differential Inclusions Driven by Hemivariational Inequalities

  • Yong-Ki Ma,
  • Sumati Kumari Panda,
  • Anurag Shukla,
  • V. Vijayakumar

摘要

This paper investigates the problem of approximate controllability for a class of Sobolev type second order impulsive differential inclusions governed by hemivariational inequalities in Hilbert spaces. The considered system incorporates both impulsive effects and nonsmooth dynamics arising from the Clarke subdifferential framework. By employing the theory of cosine operator families, multivalued analysis, and fixed point techniques, we establish sufficient conditions for the existence of mild solutions and derive approximate controllability conditions. Furthermore, we demonstrate the impulses and hemivariational inequalities influence the controllability behavior of the system. Finally, a theoretical example is provided to illustrate the applicability of the developed controllability results.