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≤y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\le y$$\end{document}) and reverse ordered (y≤x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ y\le x$$\end{document}) cases for both positive and negative values of sup∂f∂w\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sup \left( \frac{\partial f}{\partial w}\right) $$\end{document}. Established results are verified with the help of some examples.