The Equation f′′′ + ff′′ + g(f′) = 0 and the Associated Boundary Value Problems

We study the concave and convex solutions of the third order similarity differential equation f′′′ + ff′′ + g(f′) = 0, and especially the ones that satisfies the boundary conditions f(0) = a, f′(0) = b and f′(t) → λ as t → + ∞, where λ is a root of the function g. According to the sign of g between b and λ, we obtain results about existence, uniqueness and boundedness of solutions to this boundary value problem, that we denote by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${({\mathcal P}_{{\bf g};a,b,\lambda})}$$\end{document}. In this way, we pursue and complete the study done in 2008.