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HYBRID FIXED POINT THEORY AND EXISTENCE OF EXTREMAL SOLUTIONS FOR PERTURBED NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
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 Title & Authors
HYBRID FIXED POINT THEORY AND EXISTENCE OF EXTREMAL SOLUTIONS FOR PERTURBED NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
Dhage, Bapurao C.;
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 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;
 Language
English
 Cited by
1.
Hybrid fixed point result for lipschitz homomorphisms on quasi-Banach algebras, Analysis in Theory and Applications, 2011, 27, 2, 109  crossref(new windwow)
 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 crossref(new window)

3.
B. C. Dhage, A general multi-valued hybrid fixed point theorem and perturbed differential inclusions, Nonlinear Anal. 64 (2006), no. 12, 2747-2772 crossref(new window)

4.
K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985

5.
A. Granas and J. Dugundji, Fixed point theory, Springer Monographs in Mathematics. Springer-Verlag, New York, 2003

6.
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

7.
J. K. Hale, Theory of Functional Differential Equations, Springer, New York, 1977

8.
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

9.
J. Henderson, Boundary value problems for functional-differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1995

10.
M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, 1964

11.
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

12.
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 crossref(new window)

13.
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

14.
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 crossref(new window)

15.
E. Zeidler, Nonlinear Functional Analysis: Part I, Springer Verlag, New York, 1985