Existence and Approximate Controllability Results for the Second-Order Abstract Neutral Differential System with Damping

• Autores: W. Kavitha Williams, Velusamy Vijayakumar
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we investigate the approximate controllability of mild solutions for second-order differential systems. Using principles and ideas from the theory of the cosine family of operators and the fixed-point approach, we verify the existence of mild solutions for the given system. A new set of sufficient conditions is formulated and proved for the approximate controllability of second-order differential systems under the assumption that the associated linear part of the system is approximately controllable. In addition, we extend our system with nonlocal conditions. Our research on approximate controllability was also extended by utilizing impulse systems. To demonstrate the theory of the primary outcomes, an application is shown.

• Referencias bibliográficas
  • 1. Arthi, G., Balachandran, K.: Controllability of damped second-order neutral functional differential systems with impulses. Taiwan. J. Math....
  • 2. Arthi, G., Balachandran, K.: Controllability of second-order impulsive evolution systems with infinite delay. Nonlinear Anal. Hybrid Syst...
  • 3. Bainov, D.D., Lakshmikantham, V., Simeonov, P.S.: Theory of impulsive differential equations. World Scientific, Singapore (1989)
  • 4. Benchohra, M., Henderson, J., Ntouyas, S.K., Quahab, A.: Existence results for impulsive semilinear damped differential inclusions. Electron....
  • 5. Dhage, B., Dhage, J.: Approximating positive solutions of nonlinear BVPs of ordinary second-order hybrid differential equations. Malaya...
  • 6. Diop, M.A., Fall, M., Bodjrenou, F., Ogouyandjou, C.: Existence and controllability results for an impulsive stochastic integro-differential...
  • 7. Fattorini, H.O.: Second Order Linear Differential Equations in Banach Spaces. North-Holland, Amsterdam (1985)
  • 8. Hernandez, E., Balachandran, K., Annapoorani, N.: Existence results for a damped second order abstract functional differential equation...
  • 9. Jawahdou, A.: Existence of mild solutions of second-order impulsive differential equations in Banach spaces. Malaya J. Mat. 11(02), 117–126...
  • 10. Kisynski, J.: On cosine operator functions and one parameter group of operators. Stud. Math. 49, 93–105 (1972)
  • 11. Mahmudov, N.I.: Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces. SIAM J....
  • 12. Mahmudov, N.I., Denker, A.: On controllability of linear stochastic systems. Int. J. Controls 73, 144– 151 (2000)
  • 13. Sakthivel, R., Ren, Y., Mahmudov, N.I.: Approximate controllability of second-order stochastic differential equations with impulsive effects....
  • 14. Sadovskii, B.N.: On a fixed point principle. Funct. Anal. Appl. 1, 74–76 (1967)
  • 15. Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1985)
  • 16. Sathya, R., Balachandran, K.: Controllability of damped second-order neutral impulsive stochastic functional differential systems with...
  • 17. Shukla, A., Sukavanam, N., Pandey, D.N.: Controllability of semilinear stochastic control system with finite delay. IMA J. Math. Control....
  • 18. Shukla, A., Sukavanam, N., Pandey, D.N.: Complete controllability of semilinear stochastic systems with delay in both state and control....
  • 19. Shukla, A., Sukavanam, N.: Interior approximate controllability of second order semilinear control systems. Int. J. Control (2022). https://doi.org/10.1080/00207179.2022.2161013
  • 20. Travis, C.C., Webb, G.F.: Compactness, regularity and uniform continuity properties of strongly continuous cosine families. Houst. J....
  • 21. Travis, C.C., Webb, G.F.: Cosine families and abstract nonlinear second order differential equations. Acta Math. Acad. Sci. Hung. 32,...
  • 22. Vijayakumar, V.: Approximate controllability results for impulsive neutral differential inclusions of Sobolev-type with infinite delay....