Solvability and controllability of second-order non-autonomous impulsive neutral evolution hemivariational inequalities

Yong-Ki Ma; N. Valliammal; K. Jothimani; V. Vijayakumar; Yong-Ki Ma; N. Valliammal; K. Jothimani; V. Vijayakumar

doi:10.3934/math.20241288

AIMS Mathematics

2024, Volume 9, Issue 10: 26462-26482. doi: 10.3934/math.20241288

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Solvability and controllability of second-order non-autonomous impulsive neutral evolution hemivariational inequalities

1.
Department of Applied Mathematics, Kongju National University, Chungcheongnam-do 32588, Korea
2.
Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore 641202, Tamil Nadu, India
3.
Department of Mathematics, Sri G.V.G. Visalakshi College for Women, Udumalpet 642128, Tamil Nadu, India
4.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India

Received: 11 July 2024 Revised: 03 September 2024 Accepted: 05 September 2024 Published: 12 September 2024
MSC : 34K30, 35R10, 35R12, 35R70, 93B05

The primary aim of this article was to explore the approximate controllability of second-order impulsive hemivariational inequalities with initial conditions in Hilbert space. The mild solution was initially derived using the properties of the cosine and sine family of operators, Clarke's subdifferential, and the fact that the related linear equation has an evolution operator. The results of the approximate controllability of the considered systems were then taken into account using the fixed-point theorem method. An application was provided to support our theoretical findings.
- existence,
- approximate controllability,
- generalized Clarke's subdifferential,
- hemivariational inequalities
Citation: Yong-Ki Ma, N. Valliammal, K. Jothimani, V. Vijayakumar. Solvability and controllability of second-order non-autonomous impulsive neutral evolution hemivariational inequalities[J]. AIMS Mathematics, 2024, 9(10): 26462-26482. doi: 10.3934/math.20241288

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Abstract

The primary aim of this article was to explore the approximate controllability of second-order impulsive hemivariational inequalities with initial conditions in Hilbert space. The mild solution was initially derived using the properties of the cosine and sine family of operators, Clarke's subdifferential, and the fact that the related linear equation has an evolution operator. The results of the approximate controllability of the considered systems were then taken into account using the fixed-point theorem method. An application was provided to support our theoretical findings.

References

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