Monotone Iterative Techniques and a Periodic Boundary Value Problem for First Order Differential Equations with a Functional Argument

Abstract

This paper is concerned with periodic boundary value problems involving first order differential equations with functional arguments. The main feature of the paper is that the existence of maximal and minimal solutions is obtained by constructing sequences of upper and lower solutions of the initial value problems and not by establishing the comparison principle.

A modified two-sided approximation method for a four-point Vallée-Poussin type problem

“…These methods include the two-sided methods, which give provide a possibility to construct approximate solutions and, on every step of iteration, obtain a posteriori error estimates of the successive approximations. Numerous research papers are devoted to the construction of new modifications of two-sided methods aimed at the study of various boundary value problems for ordinary differential equations (see, e. g., [1][2][3]9]. This paper is devoted to the investigation of a four-point boundary-value problem of the Vallée-Poussin type for a system of non-linear differential equations with argument deviation by using a suitable version of the two-sided method generalising the works [5,6].…”