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

This article deals with a class of three-point nonlinear boundaryvalue 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.

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