A Picard method without Lipschitz continuity for some ordinary differential equations (Q1364293)

Consider an initial value problem to the scalar differential equation \(y^{(m)} (x)= f(x,y)\) where \(f\) may fail to be Lipschitzian in \(y\) or even to be continuous. The author derives conditions on \(f\) (which imply e.g. a certain asymptotic behavior in \(x\)) such that existence and uniqueness can be proved by means of a modified Picard iteration.