Open Access

Regularization of singular Sturm-Liouville equations

Abstract

The paper deals with the singular Sturm-Liouville expressions $$l(y) = -(py')' + qy$$ with the coefficients $$q = Q', \quad 1/p, Q/p, Q^2/p \in L_1,$$ where the derivative of the function $Q$ is understood in the sense of distributions. Due to a new regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent approximation is investigated and all self-adjoint and maximal dissipative extensions and generalized resolvents are described in terms of homogeneous boundary conditions of the canonical form.

Article Information

 Title Regularization of singular Sturm-Liouville equations Source Methods Funct. Anal. Topology, Vol. 16 (2010), no. 2, 120-130 MathSciNet MR2667807 zbMATH 1221.47083 Copyright The Author(s) 2010 (CC BY-SA)

Authors Information

Andrii Goriunov
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Citation Example

Andrii Goriunov and Vladimir Mikhailets, Regularization of singular Sturm-Liouville equations, Methods Funct. Anal. Topology 16 (2010), no. 2, 120-130.

BibTex

@article {MFAT545,
AUTHOR = {Goriunov, Andrii and Mikhailets, Vladimir},
TITLE = {Regularization of singular Sturm-Liouville equations},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {16},
YEAR = {2010},
NUMBER = {2},
PAGES = {120-130},
ISSN = {1029-3531},
MRNUMBER = {MR2667807},
ZBLNUMBER = {1221.47083},
URL = {http://mfat.imath.kiev.ua/article/?id=545},
}