DOI QR코드

DOI QR Code

HYBRID FIXED POINT THEORY AND EXISTENCE OF EXTREMAL SOLUTIONS FOR PERTURBED NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Dhage, Bapurao C. (KASUBAI, GURUKUL COLONY)
  • Published : 2007.05.31

Abstract

In this paper, some hybrid fixed point theorems are proved which are further applied to first and second order neutral functional differential equations for proving the existence results for the extremal solutions under the mixed Lipschitz, compactness and monotonic conditions.

Keywords

Neutral functional differential equation;extremal solutions

References

  1. B. C. Dhage, Existence theory for nonlinear functional perturbed differential equations, Nonlinear Anal. Forum 10 (2005), no. 1, 69-80
  2. B. C. Dhage, Existence of extremal solutions for discontinuous functional integral equations, Appl. Math. Lett. 19 (2006), no. 9, 881-886 https://doi.org/10.1016/j.aml.2005.08.023
  3. B. C. Dhage, A general multi-valued hybrid fixed point theorem and perturbed differential inclusions, Nonlinear Anal. 64 (2006), no. 12, 2747-2772 https://doi.org/10.1016/j.na.2005.09.013
  4. A. Granas and J. Dugundji, Fixed point theory, Springer Monographs in Mathematics. Springer-Verlag, New York, 2003
  5. A. Granas, R. B. Guenther, and J. W. Lee, Some general existence principles in the Caratheodory theory of nonlinear differential systems, J. Math. Pures Appl. (9) 70 (1991), no. 2, 153-196
  6. S. Heikkila and V. Lakshmikantham, Monotone iterative techniques for discontinuous nonlinear differential equations, Monographs and Textbooks in Pure and Applied Mathematics, 181. Marcel Dekker, Inc., New York, 1994
  7. J. Henderson, Boundary value problems for functional-differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1995
  8. M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, 1964
  9. S. K. Ntouyas, Initial and boundary value problems for functional-differential equations via the topological transversality method: a survey, Bull. Greek Math. Soc. 40 (1998), 3-41
  10. Y. G. Sficas and S. K. Ntouyas, A two-point boundary value problem for neutral functional-differential equations, Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), no. 3-4, 331-338
  11. S. K. Ntouyas and P. Ch. Tsamatos, Global existence for functional integro-differential equations of delay and neutral type, Appl. Anal. 54 (1994), no. 3-4, 251-262 https://doi.org/10.1080/00036819408840281
  12. E. Zeidler, Nonlinear Functional Analysis: Part I, Springer Verlag, New York, 1985
  13. K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985
  14. J. K. Hale, Theory of Functional Differential Equations, Springer, New York, 1977
  15. S. K. Ntouyas, Y. G. Sficas, and P. Ch. Tsamatos, Existence results for initial value problems for neutral functional-differential equations, J. Differential Equations 114 (1994), no. 2, 527-537 https://doi.org/10.1006/jdeq.1994.1159

Cited by

  1. Hybrid fixed point result for lipschitz homomorphisms on quasi-Banach algebras vol.27, pp.2, 2011, https://doi.org/10.1007/s10496-011-0109-4