Approximate controllability of nonconvex valued semilinear differential inclusion

Bholanath Kumbhakar; Dwijendra Narain Pandey

doi:10.3934/eect.2024047

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2025, Volume 14, Issue 1: 96-122. Doi: 10.3934/eect.2024047

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Approximate controllability of nonconvex valued semilinear differential inclusion

Bholanath Kumbhakar and
Dwijendra Narain Pandey^,

Indian Institute of Technology Roorkee, India

^*Corresponding author: Dwijendra Narain Pandey
^*Corresponding author: Dwijendra Narain Pandey

Received: May 2024

Early access: August 28, 2024

Published online: August 28, 2024

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Abstract

In this paper, we consider the approximate controllability of semilinear differential inclusion featuring multivalued nonlinearities with nonconvex values. Initially, we explore the approximate controllability result by assuming the underlying state space to be a super-reflexive Banach space. Then, we relax the super-reflexivity condition and prove the approximate controllability in reflexive Banach spaces by employing the relaxation technique. Incorporating multivalued maps with nonconvex values adds complexity to the studied differential inclusions yet enhances their practical applicability, serving as the core motivation for this research endeavor. We conclude by presenting an illustrative example that satisfies the criteria outlined in this paper.

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Mathematics Subject Classification: Primary: 34A60, 93B05; Secondary: 34H05.

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