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Sturm–Liouville Theory. Mathematical Surveys and Monographs
- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2020
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266120060026
- Publisher site
- See Article on Publisher Site
Abstract
We consider expressions \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {L}_k[y]$$\end{document}that are ordered products of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k$$\end{document}, \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k\in \mathbb {N}$$\end{document}, linear symmetric quasidifferential expressions ofthe second order with matrix coefficients. Asymptotic formulas as \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$x\to +\infty$$\end{document} are derived for one of the fundamental solutionsystems of the equation \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {L}_k[y]=\lambda y$$\end{document}, \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda \in \mathbb {C}$$\end{document}, \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda \ne 0$$\end{document}, undersome conditions on the behavior at infinity of its coefficients. The result is applied to the study ofspectral properties of operators generated by the expression \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {L}_k[y]$$\end{document}, and, in particular, to second-order matrixdifferential operators of the Sturm–Liouville type.
Journal
Differential Equations – Springer Journals
Published: Jun 5, 2020