Deficiency Values for the Solutions of Differential Equations with Branching Point - Mokhonko, A. Z.; Mokhonko, A. A. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
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|