Solvability and controllability of second-order non-autonomous impulsive neutral evolution hemivariational inequalities-Reference-Cited by-同舟云学术

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

Published:2024 Issue:10 Volume:9 Page:26462-26482
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ma Yong-Ki¹,Valliammal N.²,Jothimani K.³,Vijayakumar V.⁴

Affiliation:

1. Department of Applied Mathematics, Kongju National University, Chungcheongnam-do 32588, Republic of 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

Abstract

<p>The primary aim of this article is 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 are then taken into account using the fixed-point theorem method. An application is provided to support our theoretical findings.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference36 articles.

1. Y. Huang, Z. Liu, B. Zeng, Optimal control of feedback control systems governed by hemivariational inequalities, Comput. Math. Appl., 70 (2015), 2125–2136. https://doi.org/10.1016/j.camwa.2015.08.029

2. P. D. Panagiotopoulos, Hemivariational inequalities: applications in mechanics and engineering, Berlin: Springer, 1993. https://doi.org/10.1007/978-3-642-51677-1

3. P. D. Panagiotopoulos, Non-convex superpotentials in the sense of F.H. Clarke and applications, Mech. Res. Commun., 8 (1981), 335–340. https://doi.org/10.1016/0093-6413(81)90064-1

4. S. Carl, D. Motreanu, Extremal solutions of quasilinear parabolic inclusions with generalized Clarke's gradient, J. Differ. Equations, 191 (2003), 206–233. https://doi.org/10.1016/S0022-0396(03)00022-6

5. S. Carl, Existence of extremal solutions of boundary hemivariational inequalities, J. Differ. Equations, 171 (2001), 370–396. https://doi.org/10.1006/jdeq.2000.3845