Approximating positive solutions of nonlinear IVPs of ordinary second order hybrid differential equations

Bapurao Dhage; Janhavi B Dhage

doi:10.26637/mjm0902/002

Abstract

In this paper we prove the existence and approximation of solution for a nonlinear initial value problem of ordinary second order hybrid differential equation. The right hand side of the differential equation is assumed to be Caratho\`eodory and the proof is based on the Dhage iteration method

Keywords:

Nonlinear initial value problems, Hybrid differential equation, Dhage iteration method, Existence and approximation theorem.

Mathematics Subject Classification:

34A45, 34B15, 47H07 , 47H10

Authors Imprint References Funding Related Articles Downloads

Bapurao Dhage “Kasubai”, Gurukul Colony, Thodga Road, Ahmedpur- 413 515, Dist. Latur, Maharashtra, India. https://orcid.org/0000-0002-2353-8618
Janhavi B Dhage “Kasubai”, Gurukul Colony, Thodga Road, Ahmedpur- 413 515, Dist. Latur, Maharashtra, India.

Pages: 12-19
Date Published: 01-04-2021
Vol. 9 No. 02 (2021): Malaya Journal of Matematik (MJM)

K. Deimling, Nonlinear Functional Analysis, Springer Verlag, 1985.

https://doi.org/10.1007/978-3-662-00547-7

B.C. Dhage, Nonlinear functional boundary value problems involving Carathe'odory, Kyungpook Mathematical Journal, 46(2006), 421-441.

B.C. Dhage, Partially condensing mappings in partially ordered normed linear spaces and applications to functional integral equations, Tamkang Journal of Mathematics, 45(4)(2014), 397-427.

https://doi.org/10.5556/j.tkjm.45.2014.1512

B.C. Dhage, Coupled and mixed coupled hybrid fixed point principles in a partially ordered Banach algebra and PBVPs of nonlinear coupled quadratic differential equations, Differ. Equ. Appl., 11(1)(2019), 1-85.

https://doi.org/10.7153/dea-2019-11-01

B.C. Dhage, S.B. Dhage, Approximating solutions of nonlinear second order ordinary differential equations, Malaya Journal of Matematik, 4(1)(2016), 8-18.

B.C. Dhage, S.B. Dhage, Approximating soltions of PBVPs of second order ordinary differential equations via hybrid fixed point theory, Electronic J. Diff. Equations, 20(1)(2015), 1-10.

B. C. Dhage, M. Imdad, Asymptotic behaviour of nonlinear quadratic functional integral equations involving Carathe'odory, Nonlinear Analysis 71 (2009), 1285-1291.

https://doi.org/10.1016/j.na.2009.01.132

A. Granas, Fixed Point Theory, Springer Verlag 2003.

https://doi.org/10.1007/978-0-387-21593-8