On the spectrum of a second-order periodic differential equation

Coskun H.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, cilt.33, sa.4, ss.1261-1277, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 4
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1216/rmjm/1181075461
  • Dergi Adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1261-1277
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.