Existence of solutions to first-order singular and nonsingular initial value problems

Abstract

Under barrier strip type arguments we investigate the existence of global solutions to the initial value problem $x'=f(t,x,x')$, $x(0)=A$, where the scalar function $f(t,x,p)$ may be singular at $t=0$.

Keywords

• Initial value problem
• first order differential equation
• singularity
• sign conditions