Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 11
149
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Results on controllability and well-posedness of functional abstract second-order differential equations with state-dependent delay

, &
Pages 3185-3198 | Received 22 May 2022, Accepted 12 Aug 2022, Published online: 01 Sep 2022

References

  • Arjunan MM, Nadaf NY. Existence and controllability results of damped second order impulsive functional differential systems with state-dependent delay. Opusc Math. 2014;34(3):503–522.
  • Li M, Huang M. Approximate controllability of second-order impulsive stochastic differential equations with state-dependent delay. J Appl Anal Comput. 2018;8:598–619.
  • Vijayakumar V, Murugesu R. Controllability for a class of second-order evolution differential inclusions without compactness. Appl Anal. 2019;98:1367–1385.
  • Sakthivel R, Anandhi ER, Mahmudov NI. Approximate controllability of second-order systems with state-dependent delay. Numer Funct Anal Optim. 2008;29:1347–1362.
  • Aiello WG, Freedman HI, Wu J. Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J Appl Math. 1992;52:855–869.
  • Driver RD. A neutral system with state-dependent delay. J Differ Equ. 1984;54:73–86.
  • Hartung F, Turi J. On differentiability of solutions with respect to parameters in state-dependent delay equations. J Differ Equ. 1997;135:192–237.
  • Hartung F. Differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays. J Math Anal Appl. 2006;324:504–524.
  • Hartung F, Krisztin T, Walther HO, et al. Functional differential equations with state-dependent delays: theory and applications. Handb Differ Equ. 2006;3:435–545.
  • Hernández E, Prokopczyk A, Ladeira L. A note on partial functional differential equations with state-dependent delay. Nonlinear Anal. 2006;7:510–519.
  • Kosovalic N, Magpantay FMG, Chen Y, et al. Abstract algebraic-delay differential systems and age structured population dynamics. J Differ Equ. 2013;255:593–609.
  • Rezounenko AV. A condition on delay for differential equations with discrete state-dependent delay. J Math Anal Appl. 2012;385:506–516.
  • Rezounenko AV. Partial differential equations with discrete and distributed state-dependent delays. J Math Anal Appl. 2007;326:1031–1045.
  • Rezounenko AV, Wu J. A non-local PDE model for population dynamics with state-selective delay: local theory and global attractors. J Comput Appl Math. 2006;190:99–113.
  • Hernández E, Azevedo K, O'Regan D. On second order differential equations with state-dependent delay. Appl Anal. 2018;97:2610–2617.
  • Krisztin T, Rezounenko A. Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold. J Differ Equ. 2016;260:4454–4472.
  • Hernández E, Pierri M, Wu J. C1+α-strict solutions and well-posedness of abstract differential equations with state-dependent delay. J Differ Equ. 2016;261:6856–6882.
  • Kosovalic N, Chen Y, Wu J. Algebraic-delay differential systems: C0-extendable submanifolds and linearization. Trans Am Math Soc. 2017;369:3387–3419.
  • Lv Y, Yuan R, Pei Y. Smoothness of semiflows for parabolic partial differential equations with state-dependent delay. J Differ Equ. 2016;260:6201–6231.
  • Ruggieri M, Santra SS, Scapellato A. Oscillatory behavior of second-order neutral differential equations. Bull Braz Math Soc. 2021;doi:10.1007/s00574-021-00276-3 .
  • Ruggieri M, Santra SS, Scapellato A. On nonlinear impulsive differential systems with canonical and non-canonical operators. Appl Anal. 2021;doi:10.1080/00036811.2021.1965586 .
  • Santra SS, Scapellato A. Some conditions for the oscillation of second-order differential equations with several mixed delays. J Fixed Point Theory Appl. 2022;24(1):18.
  • Buga M, Martin M. The escaping disaster: a problem related to state-dependent delays. Z Angew Math Phys. 2004;55:547–574.
  • Si JG, Wang XP. Analytic solutions of a second-order functional-differential equation with a state derivative dependent delay. Colloq Math. 1999;79:273–281.
  • Chueshov I, Rezounenko A. Dynamics of second order in time evolution equations with state-dependent delay. Nonlinear Anal. 2015;123–124:126–149.
  • Das S, Pandey DN, Sukavanam N. Existence of solution and approximate controllability of a second-order neutral stochastic differential equation with state-dependent delay. Acta Math Sci. 2016;36:1509–1523.
  • Hernández E. Existence of solutions for a second order abstract functional differential equation with state-dependent delay. Electron J Differ Equ. 2007;21:1–10.
  • Radhakrishnan B, Balachandran K. Controllability of neutral evolution integrodifferential systems with state-dependent delay. J Optim Theory Appl. 2012;153:85–97.
  • Vijayakumar V, Udhayakumar R, Dineshkumar C. Approximate controllability of second order nonlocal neutral differential evolution inclusions. IMA J Math Control Inf. 2020;38(1):192–210.
  • Vijayakumar V, Henríquez HR. Existence of global solutions for a class of abstract second-order nonlocal cauchy problem with impulsive conditions in Banach spaces. Numer Funct Anal Optim. 2018;39:704–736.
  • Hino Y, Murakami S, Naito T. Functional-differential equations with infinite delay. Springer-Verlag: Berlin; 1991. (Lecture notes in mathematics).
  • Kisyński J. On cosine operator functions and one parameter group of operators. Stud Math. 1972;44:93–105.
  • Travis CC, Webb GF. Cosine families and abstract nonlinear second order differential equations. Acta Math Acad Sci Hung. 1978;32:75–96.
  • Vasil'ev VV, Piskarev SI. Differential equations in Banach spaces. II. Theory of cosine operator functions. J Math Sci. 2004;122:3055–3174.
  • Arthi G, Balachandran K. Controllability of second order impulsive functional differential equations with state-dependent delay. Bull Korean Math Soc. 2011;48:1271–1290.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.