Existence of solutions to an initial value problem for the differential equation \(f(t,x,x^{\prime})=0\) using barrier strips (Q885322)

Sufficient conditions guaranteeing the existence of global solutions to the singular initial value problem \[ f(t,x,x')= 0,\quad x(0)= A \] are presented by using barrier strips. Throughout the paper it is assumed that the function \(f(t,x,p)\) is defined for \((t,x,p)\in D_t\times \{D_x\setminus\{A\}\}\times D_p\). It may be singular at \(x=A\). The sets \(D_t\), \(D_x\), \(D_p\subseteq R\) may be bounded, \(D_x\) is such that \(A\) is an interior point.