AN ABSTRACT MODEL OF LINEAR DIFFERENTIAL TRANSFORMATЮNS

Owing to the Sturm separation theorem the exact distribution of zeros for integrals of 2nd order linear differential equations in the real domain can be described by means of certain functions. The study of these functions is in a close connection with transformations Y(t) = = m(t)y(a(t)) of solutions y and Y of the equations y " = q(t)y and Y " = Q(t)Y. These both problems meet in the 3rd order non-linear differential equations of the form ( q, 0- { M} + * a ' 2 =Q(t). The corresponding algebraic behaviour has been described in [1], particularly in great detail for both-sided oscillatory equations in R. In this paper we present an abstract model which is directly applicable to the just mentioned case. The other possible applications can be expected in two directions, first for the general case of 2nd order transformations and secondly for the transforma-tions of nth order lineare quations. GENERAL SYMBOL