ABSTRACT
In the beginning of this chapter, the concept of Azbelev's approach to the definition of a homogeneous equation is discussed. This concept allows us to study delay and functional differential equations in the finite space of solutions. This opens possibilities to use the classical notions of the theory of ordinary differential equations. One of the main of them is the Wronskian of the fundamental system. This book is the first one, where the Wronskian of the fundamental system for functional differential equations is studied. Chapters 10, 12,13 and 14 are devoted to the study of the various properties of the Wronskian. Non-vanishing of the Wronskian for the second order functional differential equations is equivalent to the validity of the Sturm separation theorem: between every two adjacent zeros of nontrivial solution of the homogeneous equations there is one and only one zero of every other non-proportional solution. The validity of the Sturm theorem for neutral delay equations is obtained under assumptions on the smallness of delays.
