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Keywords:
linear differential equations; distribution of zeros; asymptotic behaviour; Abel’s functional equation
linear differential equations; distribution of zeros; asymptotic behaviour; Abel’s functional equation
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.
References:
[1] E. Barvínek: O rozložení nulových bodů řešení lineární diferenciální rovnice $y^{\prime \prime }=Q(t)y$ a jejich derivací. Acta F. R. N. Univ. Comenian 5 (1961), 465–474.
[2] O. Borůvka: Linear Differential Transformations of the Second Order. The English Univ. Press, London, 1971. MR 0463539
[3] B. Choczewski: On differentiable solutions of a functional equation. Ann. Polon. Math. 13 (1963), 133–138. MR 0153998
[4] M. Kuczma: Functional Equations in a Single Variable. PWN, Warszawa, 1968. MR 0228862 | Zbl 0196.16403
[5] F. Neuman: Distribution of zeros of solutions of $y^{\prime \prime } = q(t)y$ in relation to their behaviour in large. Studia Sci. Math. Hungar 8 (1973), 177–185. MR 0333344 | Zbl 0286.34050
[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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