Chinese Annals of Mathematics, Series B

, Volume 41, Issue 1, pp 27–36

# Properties of Complex Oscillation of Solutions of a Class of Higher Order Linear Differential Equations

Article

## Abstract

Let A(z) be an entire function with $$\mu (A) < \tfrac{1}{2}$$ such that the equation f(k) + A(z)f = 0, where k ≥ 2, has a solution f with λ(f) < μ(A), and suppose that A1 = A + h, where h ≢ 0 is an entire function with ρ(h) < μ(A). Then g(k) + A1(z)g = 0 does not have a solution g with λ(g) < ∞.

## Keywords

Complex differential equations Entire function Order of growth Exponent of convergence of the zeros

34M10 30D35

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