ABSTRACT
This chapter discusses the optimal control problems for some first and second order differential equations. It discusses the first order case that is subject to anti-periodic boundary problems for nonlinear ordinary differential equations of a specific form. The second order case is subject to “elliptic type” linear equations. The chapter discusses the existence of the optimal pair and the necessary conditions for the pair to be an optimal pair. It obtains the existence, uniqueness and continuous dependence (via monotonicity method) of a specific solution, and then discusses the necessary and sufficient condition for the pair to be the optimal pair.
