2017
Том 69
№ 9

All Issues

Deficiency Values for the Solutions of Differential Equations with Branching Point

Mokhon'ko A. Z., Mokhon'ko O. A.

Full text (.pdf)


Abstract

We study the distribution of values of the solutions of an algebraic differential equation P(z, f, f′, . . . , f (s)) = 0 with the property that its coefficients and solutions have a branching point at infinity (e.g., a logarithmic singularity). It is proved that if a ∈ ℂ is a deficiency value of f and f grows faster than the coefficients, then the following identity takes place: P(z, a, 0, . . . , 0) ≡ 0, z ∈ {z : r 0|z| < ∞}. If P(z, a, 0, . . . , 0) is not identically equal to zero in the collection of variables z and a, then only finitely many values of a can be deficiency values for the solutions fM b with finite order of growth.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 7, pp 1048-1069.

Citation Example: Mokhon'ko A. Z., Mokhon'ko O. A. Deficiency Values for the Solutions of Differential Equations with Branching Point // Ukr. Mat. Zh. - 2014. - 66, № 7. - pp. 939–957.

Full text