On the boundary value problem for the Sturm-Liouville equation with the discontinuous coefficient

Nabiev A. A. , AMİROV R.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.36, sa.13, ss.1685-1700, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 36 Konu: 13
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1002/mma.2714
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Sayfa Sayıları: ss.1685-1700

Özet

We consider a boundary value problem for the Sturm-Liouville equation with piecewise-constant leading coefficient. We prove that some integral representations for the solutions of the considered equation can be obtained by using classical transformation operators for the Sturm-Liouville operator at the end points of a finite interval. We also investigate thespectral characteristics of the boundary value problem, prove the completeness and expansion theorem. Copyright (c) 2012 John Wiley & Sons, Ltd.