A Method of Lower and Upper Solutions for Control Problems and Application to a Model of Bone Marrow Transplantation

Abstract

A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka–Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.

Keywords

• control problem
• lower and upper solutions
• fixed point
• approximation algorithm
• numerical solution
• medical application