Electron. J. Diff. Equ., Vol. 2015 (2015), No. 20, pp. 1-10.

Approximating solutions of nonlinear PBVPs of second-order differential equations via hybrid fixed point theory

Bapurao C. Dhage, Shyam B. Dhage

Abstract:
In this article we prove the existence and approximations of solutions of periodic boundary-value problems of second-order ordinary nonlinear hybrid differential equations. We rely our results on Dhage iteration principle or method embodied in a recent hybrid fixed point theorem of Dhage (2014) in partially ordered normed linear spaces. Our resutls are proved under weaker continuity and Lipschitz conditions. An example illustrates the theory developed in this article.

Submitted November 6, 2014. Published January 27, 2015.
Math Subject Classifications: 34A12, 34A38.
Key Words: Hybrid differential equation; periodic boundary value problems; Dhage iteration method; hybrid fixed point theorem; approximate solution.

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Bapurao C. Dhage
Kasubai, Gurukul Colony, Ahmedpur-413 515
Dist: Latur Maharashtra, India
email: bcdhage@gmail.com
Shyam B. Dhage
Kasubai, Gurukul Colony, Ahmedpur-413 515
Dist: Latur Maharashtra, India
email: sbdhage4791@gmail.com

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