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

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## 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## 2000 MR Subject Classification

34M10 30D35## Preview

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