MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.36, no.13, pp.1685-1700, 2013 (SCI-Expanded)
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.