Monotone iterations for differential problems (Q2770611)

In this survey paper, results on the existence and construction of minimal, maximal and unique solutions to the first-order differential equation with parameter NEWLINE\[NEWLINEx'(t)=f(t,x(t),\lambda),\;t\in J=[0,b],\quad x(0)=k_0\in \mathbb{R},\;G(x(b),\lambda)=0,NEWLINE\]NEWLINE are stated, with \(f\in C(J\times \mathbb{R}\times \mathbb{R},\mathbb{R})\) and \(G\in C(\mathbb{R}\times \mathbb{R},\mathbb{R})\).