Consider the initial value problem
The author defines lower and upper solutions to and shows that under some conditions on and the existence of lower and upper solutions implies the existence of a solution to . His main interest concerns the construction of monotone sequences converging to extremal solutions of . In particular, he considers the case
where is nonincreasing in and is nondecreasing in . Using the notation of mixed lower and upper solutions, he constructs sequences which monotoneously converge to extremal mixed solutions.