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linear differential equations; distribution of zeros; asymptotic behaviour; Abel’s functional equation
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.
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[6] F. Neuman: Global Properties of Linear Ordinary Differential Equations. Mathematics and Its Applications (East European Series) 52, Kluwer Acad. Publ., Dordrecht-Boston-London, 1991, ISBN 0-7923-1269-4. MR 1192133
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