This article is cited in 11 papers

Asymptotic behavior of the solutions and nodal points of Sturm–Liouville differential expressions

A. Yu. Trynin

Saratov State University named after N. G. Chernyshevsky, Faculty of Mathematics and Mechanics, Saratov

Abstract: We obtain asymptotic formulas for the values of second-order differential operators with the coefficient of bounded variation depending on the spectral parameter. We give a counterexample showing that the requirement of boundedness for the variation is essential for the preservation of the error of the so-obtained asymptotic formulas.

Keywords: differential operator, asymptotic formula, bounded variation.

UDC: 517.5+517.925.44

Received: 30.09.2007
Revised: 27.10.2009

 English version: Siberian Mathematical Journal, 2010, 51:3, 525–536

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