Email this article POISSON PROBLEM FOR A LINEAR FUNCTIONAL DIFFERENTIAL EQUATION
- Authors: Labovskiy S.M.1, Getimane M´ario Frengue -2
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Affiliations:
- Plekhanov Russian University of Economics
- Instituto Superior de Transportes e Comunica
- Issue: Vol 21, No 1 (2016)
- Pages: 76-81
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/362911
- DOI: https://doi.org/10.20310/1810-0198-2016-21-1-76-81
- ID: 362911
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Abstract
The solvability, existence and positiveness of the Green function of the Poisson problem -∆u- Ωu y -u x r x,dy =ρf, u | Γ( Ω) =0 are showed. The spectral properties of corresponding eigenvalue problem are considered. Here Ω is an open set in R N and ΓΩ is the boundary of the Ω . For almost all x ϵ Ω, r x,∙ is a measure satisfying certain symmetry condition. The function ρ is a positive weight. This problem has a clear mechanical interpretation.
About the authors
Sergei Mikhailovich Labovskiy
Plekhanov Russian University of Economics
Email: labovski@gmail.com
Candidate of Physics and Mathematics, Associate Professor of the Higher Mathematics Department Moscow, the Russian Federation
- Getimane M´ario Frengue
Instituto Superior de Transportes e Comunica
Email: mgetimane@isutc.transcom.co.mz
Associate Professor, Mathematics Department Maputo, Mozambique
References
Labovskii S.M. On the Sturm-Liouville problem for a linear singular functional-differential equation // Russ. Math., 1996. V. 40, № 11. P. 50-56. (English. Russian original. Translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1996, № 11 (414), 48-53). Labovskii S. Little vibrations of an abstract mechanical system and corresponding eigenvalue problem // Functional Differential Equations, 1999. V. 6, № 1-2. P. 155-167. Labovskiy S. On spectral problem and positive solutions of a linear singular functional differential equation // Functional Differential Equations, 2013. V. 20, № 3-4. P. 179-200. Adams R.A. and Fournier J. Sobolev Spaces // Elsevier, 2003.
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