Monotone iterative techniques for nonlinear problems involving the difference of two monotone functions.
Consider the scalar initial value problem \((*) \;du/dt = f(t,u)+g(t,u), \;u(0)=0,\) under the condition that \(f\) is monotone increasing and \(g\) is monotone decreasing in \(u\). The authors prove a theorem on the convergence of a monotone iteration scheme provided coupled lower and upper solutions exist.
scientific article; zbMATH DE number 1861248