On the spectrum of a second-order periodic differential equation


Coskun H.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.33, no.4, pp.1261-1277, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 4
  • Publication Date: 2003
  • Doi Number: 10.1216/rmjm/1181075461
  • Title of Journal : ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1261-1277

Abstract

In this paper we derive asymptotic approximations for the periodic and semi-periodic eigenvalues for a second-order periodic differential equation known as Hill's equation. Our results are sharper than the existing results in the literature in that they give sharper error bounds whilst relaxing the smoothness assumptions. For some particular potentials, including that of Mathieu equation, we provide estimates for the corresponding eigenvalues using the symbolic manipulator package, Maple.