This article is cited in 3 papers

Mathematics

Oscillation theorems for Sturm–Liouville problems with distribution potentials

A. A. Shkalikov^a, J. Ben Amara<sup>b

a</sup> Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b University of 7-th November at Carthage, Faculte' des Sciences de Bizerte, Tunisia

Abstract: The Sturm–Liouville problem
\begin{gather*} -y''+q(x)y=\lambda y,\\ y(0)=y(1)=0 \end{gather*}
is considered with a singular potential $q(x)$ representing the derivative of a real function from the space $L_2[0,1]$ in the distributional sense. Two approaches are developed for the study of oscillation properties of eigenfunctions of this problem. The first approach is based on generalization of methods of the Sturm theory. The second one is based on development of variational principles.

Key words: Sturm–Liouville problem, singular potentials, variational methods, oscillation theory.

UDC: 517.984

Received: 16.06.2008

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