Oscillation results for n-TH order linear differential equations with meromorphic periodic coefficients

Consider n-th order linear differential equations with meromorphic periodic coefficients of the form w((n)) + Rn-1(e(z))w((n-1)) + ... + R-1 (e(z))w' + R-0(e(z))w = 0, n greater than or equal to 2, where R-v(t) (0 less than or equal to v less than or equal to n - 1) are rational functions of t. Under certain assumptions, we prove oscillation theorems concerning meromorphic solutions, which contain necessary conditions for the existence of a meromorphic solution with finite exponent of convergence of the zero-sequence. We also discuss meromorphic or entire solutions whose zero-sequences have an infinite exponent of convergence, and give a new zero-density estimate for such solutions.