We discuss existence, non-uniqueness and regularity of one- two-sided solutions initial value problems for scalar quasi-linear ordinary differential equations where the condition corresponds to an impasse point equation. With a geometric approach, we reduce problem questions in dynamical systems theory. As application, detail second-order form g(x)u?=f(x,u,u?) with imposed at simple zero g. Thi...

Recently, there are many results about the existence and multiplicity of positive solutions for nonlinear second-order differential equations(see[7],[5],[3]). Henderson and Thompson(see[4]), Li and Zhang (see[2]) studied the multiple symmetric positive and nonnegative solutions of second-order ordinary differential equations. Yao (see[6]) considered the existence and iteration of n symmetric po...

Abstract This paper focuses on second-order differential equations involving causal operators with nonlinear two-point boundary conditions. By applying the monotone iterative technique in presence of upper and lower solutions, a new comparison theorem, we obtain existence extremal solutions. is an extension classical theory equations. Finally, present two examples to show usefulness our results.

In this article Differential Transformation Method (DTMs) is considered to find exact and approximate solutions of singular Initial Value Problems (IVPs) of the Lane-Emden type in second-order Ordinary Differential Equations (ODEs). The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series so...