Electron. J. Diff. Equ., Vol. 2014 (2014), No. 173, pp. 1-11.

Existence of solutions for three-point BVPs arising in bridge design

Amit K. Verma, Mandeep Singh

Abstract:
This article deals with a class of three-point nonlinear boundary-value problems (BVPs) with Neumann type boundary conditions which arises in bridge design. The source term (nonlinear term) depends on the derivative of the solution, it is also Lipschitz continuous. We use monotone iterative technique in the presence of upper and lower solutions for both well order and reverse order case. Under some sufficient conditions we prove existence results. We also construct two examples to validate our results. These result can be used to generate a user friendly package in Mathematica or MATLAB so that solutions of nonlinear boundary-value problems can be computed.

Submitted February 25, 2014. Published August 12, 2014.
Math Subject Classifications: 34L30, 34B27, 34B15.
Key Words: Monotone iterative technique; Lipschitz continuous; reversed ordered upper and lower solutions; three point BVP; nonlinear ODE; Green's function.

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Amit Kumar Verma
Department of Mathematics, BITS Pilani
Pilani-333031, Rajasthan, India
email: amitkverma02@yahoo.co.in
Mandeep Singh
Department of Mathematics, BITS Pilani
Pilani-333031, Rajasthan, India
email: mandeep04may@yahoo.in

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