On the dependent property of solutions for general higher order periodic differential equation

In this paper, the property of linearly dependence of solutions f(z) and f(z+2πi) for higher order linear differential equationf(k)(z)+Ak−2(z)f(k−2)(z)+⋯+A0(z)f(z)=0, where Aj(z) (j=0,…,k−2) are entire periodic coefficients and As(z) (s∈{2,…,k−2}) is the dominant coefficient, is investigated.