Ordinary Differential Equations

Abstract

Many theorems of this chapter are very similar to the corresponding theorems of the preceding chapter. If we nevertheless devote a new chapter to an old subject, this will be justified by a new method. This method deals with differential equations and inequalities, whereas earlier the corresponding integral equations stood in the foreground. This is not done merely to give the old theorems a second proof. Rather, both of these first two chapters furnish, besides their concrete assertions, a methodology for later problems connected with partial differential equa­tions. Chapter III, devoted to hyperbolic differential equations, contains in essence a translation of Chapter I into several dimensions, while the theory of the parabolic equations in Chapter IV is closely connected to the present Chapter II.