On Complex Oscillation Property of Solutions for Higher-Order Periodic Differential Equations

The property of linearly dependence of solutions $f(z)$ and $f(z+2\pi \mathrm{i})$ for higher-order linear differential equations $f^{(k)}+A_{k-2}f^{(k-2)}+\cdots+A_{1}f^{'}+A_{0}f=0$ with periodic entire coefficients is investigated, where $A_{1}$ for the equation is the dominant coefficient.