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 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 4
  • Publication Date: 2003
  • Doi Number: 10.1216/rmjm/1181075461
  • Journal Name: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • 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.