On the exactness of the Kiguradze-Kvinikadze blow-up condition for nonlinear ordinary differential equations

TL;DR

This paper demonstrates the precise applicability of the Kiguradze-Kvinikadze blow-up condition to solutions of certain nonlinear ordinary differential equations, confirming its exactness for the Cauchy problem.

Contribution

It proves the exactness of the Kiguradze-Kvinikadze blow-up condition for nonlinear ODE solutions in the Cauchy problem setting.

Findings

The blow-up condition is exact for solutions of the specified nonlinear ODEs.

The result applies to initial conditions with non-negative derivatives.

It clarifies the boundary of the blow-up criterion's applicability.

Abstract

We show the exactness of the Kiguradze--Kvinikadze blow-up condition for solutions of the Cauchy problem $$ w^{(m)} = f (t, w, \ldots, w^{(m - 1)}), \qquad w^{(i)} (0) = a_i \ge 0, \quad i = 0, \ldots, m - 1. $$