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On nonlocal three-point boundary value problems of Duffing equation with mixed nonlinear forcing terms

Ahmed Alsaedi* and Mohammed HA Aqlan

Author Affiliations

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box. 80203, Jeddah 21589, Saudi Arabia

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Boundary Value Problems 2011, 2011:47  doi:10.1186/1687-2770-2011-47

Published: 25 November 2011

Abstract

In this paper, we investigate the existence and approximation of the solutions of a nonlinear nonlocal three-point boundary value problem involving the forced Duffing equation with mixed nonlinearities. Our main tool of the study is the generalized quasilinearization method due to Lakshmikantham. Some illustrative examples are also presented.

Mathematics Subject Classification (2000): 34B10, 34B15.

Keywords:
Duffing equation; nonlocal boundary value problem; quasilinearization; quadratic convergence