Abstract
Suppose that A is a transcendental entire function with \(\rho(A)<{1\over 2}\). Suppose that k ≥ 2 and y(k) + Ay = 0 has a solution ƒ with λ(ƒ) < ρ(A), and suppose that A1 = A + h where h ≢ 0 is an entire function with ρ(h) < ρ(A). Then y(k) + A1y = 0 does not have a solution g with λ(g) < ρ(A).
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