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, vol.36, no.13, pp.1685-1700, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 13
  • Publication Date: 2013
  • Doi Number: 10.1002/mma.2714
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Page Numbers: pp.1685-1700

Abstract

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.