A different monotone iterative technique for a class of nonlinear three-point BVPs

This work examines the existence of the solutions of a class of three-point nonlinear boundary value problems that arise in bridge design due to its nonlinear behavior. A maximum and anti-maximum principles are derived with the support of Green’s function and their constant sign. A different monotone iterative technique is developed with the use of lower solution x(z) and upper solution y(z). We have also discussed the classification of well ordered ( $$x\le y$$ ) and reverse ordered ( $$ y\le x$$ ) cases for both positive and negative values of $$ \sup \left( \frac{\partial f}{\partial w}\right) $$ . Established results are verified with the help of some examples.