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Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay

  • Kulandhivel Karthikeyan , Dhatchinamoorthy Tamizharasan , Thabet Abdeljawad EMAIL logo and Kottakkaran Sooppy Nisar
Published/Copyright: May 23, 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 4

Abstract

This study investigates the functional abstract second order impulsive differential equation with state-dependent delay. The major result of this study is that the abstract second-order impulsive differential equation with state-dependent delay system has at least one solution and is unique. After that, the wellposed condition is defined. Following that, we look at whether the proposed problem is wellposed. Finally, some illustrations of our findings are provided.

Keywords: cosine function; impulsive neutral equation; state dependent delay; wellposedness
Corresponding author: Thabet Abdeljawad, Department of Mathematics and Sciences, Prince Sultan University, P.O.Box 66833, Riyadh, Saudi Arabia; and Department of Medical Research, China Medical University, Taichung 40402, Taiwan, E-mail:

Acknowledgement

Author’s wish is to express their gratitude to the anonymous referees for their valuable suggestions and comments for improving this manuscript. The author T. Abdeljawad would like to thank Prince Sultan University for the support through the TAS research lab.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None.

  3. Conflict of interest statement: None.

  4. Availability of data and materials: None.

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Received: 2021-04-14
Revised: 2021-08-26
Accepted: 2022-04-18
Published Online: 2022-05-23

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0160
Keywords for this article
cosine function; impulsive neutral equation; state dependent delay; wellposedness

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Image-based 3D reconstruction precision using a camera mounted on a robot arm
  4. Switched-line network with digital phase shifter
  5. M-lump waves and their interactions with multi-soliton solutions for the (3 + 1)-dimensional Jimbo–Miwa equation
  6. Optimal control for a class of fractional order neutral evolution equations
  7. Perceptual evaluation for Zhangpu paper-cut patterns by using improved GWO-BP neural network
  8. Two new iterative schemes to approximate the fixed points for mappings
  9. Ulam’s type stability of impulsive delay integrodifferential equations in Banach spaces
  10. Generalization method of generating the continuous nested distributions
  11. Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay
  12. Numerical study of heat and mass transfer on the pulsatile flow of blood under atherosclerotic condition
  13. Dynamic propagation behaviors of pure mode I crack under stress wave loading by caustics
  14. Numerical simulation of buoyancy-induced heat transfer and entropy generation in 3D C-shaped cavity filled with CNT–Al2O3/water hybrid nanofluid
  15. On coupled system of nonlinear Ψ-Hilfer hybrid fractional differential equations
  16. Hellinger–Reissner variational principle for a class of specified stress problems
  17. Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition
  18. Fredholm determinants and Z n -mKdV/Z n -sinh-Gordon hierarchies
  19. New soliton waves and modulation instability analysis for a metamaterials model via the integration schemes
  20. A modified high-order symmetrical WENO scheme for hyperbolic conservation laws
  21. Cryptanalysis of various images based on neural networks with leakage and time varying delays
  22. Spectral collocation method approach to thermal stability of MHD reactive squeezed fluid flow through a channel
  23. Higher order Traub–Steffensen type methods and their convergence analysis in Banach spaces
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