On a problem in complex oscillation theory of periodic higher order linear differential equations

In this article, the zeros of solutions of differential equationequation(*)f(k)(z)+A(z)f(z)=0,f(k)(z)+A(z)f(z)=0,are studied, where k>2,A(z)=B(ez),B(ζ)=g1(1/ζ)k>2,A(z)=B(ez),B(ζ)=g1(1/ζ), g1 and g2 being entire functions with g2 transcendental and σ(g2) not equal to a positive integer or infinity. It is shown that any linearly independent solutions f1, f2,…, fk of Eq(*) satisfy λe(f … fk)≥ σ(g2) under the condition that fj(z) and fj(z + 2πi) (j = 1,…,k) are linearly dependent.