On the oscillation theory of periodic linear differential equations

For equations in a broad class of linear differential equations of arbitrary order having periodic coefficients, we set forth a procedure for determining large regions in the plane in which no solution f(z) ? 0 can have infinitely many zeros. This permits us to determine locations in the plane where the zeros of a solution must be concentrated. Our results apply to higher-order analogues of the well-known Mathieu equation. The class of equations we treat has been investigated in several recent papers (e.g. [6, 7, 8, 9]) from the point of view of determining the frequency of zeros of the solutions