Approximation Method for Hybrid Functional Differential Equations

	International Journal of Mathematics Trends and Technology (IJMTT)
	© 2019 by IJMTT Journal
	Volume-65 Issue-6
	Year of Publication : 2019
	Authors : S.N.SALUNKHE
	10.14445/22315373/IJMTT-V65I6P504

MLA Style:S.N.SALUNKHE "Approximation Method for Hybrid Functional Differential Equations" International Journal of Mathematics Trends and Technology 65.6 (2019): 21-25.

APA Style: S.N.SALUNKHE (2019). Approximation Method for Hybrid Functional Differential Equations International Journal of Mathematics Trends and Technology, 21-25.

Abstract
In this paper existence theorem for the Extremal solutions is proved for an initial value problem of nonlinear hybrid functional differential equations via constructive methods.

Reference
[1] G.S.Ladde,V.Lakshmikantham and A.S.Vatsala,Monotone iterative techniques for nonlinear differential equations,Pitman, New York, 1985.
[2] V.Lakshmikantham and S.Leela, Differential and Integral Inequalities, Academic press,Newyork,1969
[3] B.C.Dhage, A fixed point theorem in Banach algebras with applications to functional integral equations,Kyungpook Math.J.44(2004),145-155.
[4] B.C.Dhage and V.Lakshmikantham, Global existence and convergence theorem for hybrid differential equations (Submitted for publication)
[5] B. C. Dhage, S. N. Salunkhe, Ravi Agarwal and W. zhang, A functional differential equations in Banach algebras, Math. Inequ. Appl. 8(1) (2005), 89-99.
[6] B. C. Dhage, S. N. Salunkhe and R. U. Verma, A neutral functional differential equation in Banach Algebras. Math. Sci. Resarch. J. 9(4) (2005), 101-113.
[7] Salunkhe S. N., Timol M. G. – Positivity Results ForFunctional Differential Equations on Unbounded Intervals.VNSGU Journal of Science and Technology V1(2)- (2009),161-168.
[8] J.K.Hale,Theory of functional differential equations, Springer Verlag,New York, 19677.
[9] J.Henderson, Boundary value problems for functional differential equations, World Scientific, Singapore, 1995.

Keywords
Extremal solution, lower and upper solution, nonlinear hybrid functional differential equations, fixed point theorem