Deficiency Values for the Solutions of Differential Equations with Branching Point

  • A. Z. Mokhonko
  • A. A. Mokhonko

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.
Published
25.07.2014
How to Cite
MokhonkoA. Z., and MokhonkoA. A. “Deficiency Values for the Solutions of Differential Equations With Branching Point”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 7, July 2014, pp. 939–957, http://umj.imath.kiev.ua/index.php/umj/article/view/2190.
Section
Research articles