Dispersions for linear differential equations of arbitrary order

summary:For linear differential equations of the second order in the Jacobi form $$y^{\prime \prime } + p(x)y = 0$$ O. Borvka introduced a notion of dispersion. Here we generalize this notion to certain classes of linear differential equations of arbitrary order. Connection with Abel’s functional equation is derived. Relations between asymptotic behaviour of solutions of these equations and distribution of zeros of their solutions are also investigated