On the oscillation theory of periodic linear differential equations

Abstract

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

Keywords:

• Linear differential equation
• zeros
• q Mathieu equation

^†This research was supported in part by NSF (Dms-8721813).

^†This research was supported in part by NSF (Dms-8721813).

Notes

^†This research was supported in part by NSF (Dms-8721813).