On the Existence of a Solution of the Boundary Initial-Value Problem

TL;DR

This paper investigates conditions under which solutions to a first-order ODE initial-value problem exist or do not exist, especially when the initial point lies on the boundary of the domain.

Contribution

It provides new sufficient conditions for the existence and non-existence of solutions at boundary points of the domain for first-order ODEs.

Findings

Sufficient conditions for solution existence at boundary points

Criteria for non-existence of solutions on boundary

Analysis of solutions near boundary initial points

Abstract

An initial-value problem for an ordinary differential equation of the first order, is considered. It is supposed that the right-hand side of the equation is a continuous function defined on a set consisting of an open set and a part of its bound. Sufficient conditions of the existence and of non-existence of a solution through initial point belonging to the boundary part of the set of definition, are presented.