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

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 A ₁ = A + h, where h ≢ 0 is an entire function with ρ(h) < μ(A). Then g ^(k) + A ₁(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

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