Email this article On the spectral properties and positivity of solutions of a periodic boundary value problem for a second-order functional differential equation
- Authors: Alves M.J.1, Labovskiy S.M.2
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Affiliations:
- Eduardo Mondlane University
- Plekhanov Russian University of Economics
- Issue: Vol 25, No 130 (2020)
- Pages: 123-130
- Section: Articles
- URL: https://ogarev-online.ru/2686-9667/article/view/295071
- DOI: https://doi.org/10.20310/2686-9667-2020-25-130-123-130
- ID: 295071
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Abstract
For a functional-differential operator Lu = (1/ρ) -(pu')' + 0 l u(s) d s r(x, s) with symmetry, the completeness and orthogonality of the eigenfunctions is shown. The positivity conditions of the Green function of the periodic boundary value problem are obtained.
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About the authors
Manuel J. Alves
Eduardo Mondlane University
Email: mjalves@gmail.com
PhD in Mathematics, Full Professor of the Mathematics Department Julius Nyerere Av., Maputo 3453, Mozambique
Sergey M. Labovskiy
Plekhanov Russian University of Economics
Email: labovski@gmail.com
Candidate of Physics and Mathematics, Associate Professor of the High Mathematics Department 36, Stremyanny Lane, Moscow 117997, Russian Federation
References
- S. Labovskiy, “On spectral problem and positive solutions of a linear singular functionaldifferential equation”, Functional Differential Equations, 20:3-4 (2013), 179-200.
- S.M. Labovski˘ı, “On the Sturm-Liouville problem for a linear singular functional-differential equation”, Russ. Math., 40:11 (1996), 50-56.
- S. Labovskii, “Little vibrations of an abstract mechanical system and corresponding eigenvalue problem”, Functional Differential Equations, 6:1-2 (1999), 155-167.
- N. V. Azbelev, V.P. Maksimov, L. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations. Methods and Applications., Hindawi Publishing Corporation, New York, 2007.
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