Periodic Problems of Difference Equations and Ergodic Theory
The necessary and sufficient conditions for solvability of the family of difference equations with periodic boundary condition were obtained using the notion of relative spectrum of linear bounded operator in the Banach space and the ergodic theorem. It is shown that when the condition of existence...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/928587 |
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| _version_ | 1832551066872315904 |
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| author | B. A. Biletskyi A. A. Boichuk A. A. Pokutnyi |
| author_facet | B. A. Biletskyi A. A. Boichuk A. A. Pokutnyi |
| author_sort | B. A. Biletskyi |
| collection | DOAJ |
| description | The necessary and sufficient conditions for solvability of the family of difference equations with periodic boundary condition were obtained using the notion of relative spectrum of linear bounded operator in the Banach space and the ergodic theorem. It is shown that when the condition of existence is satisfied, then such periodic solutions are built using the formula for the generalized inverse operator to the linear limited one. |
| format | Article |
| id | doaj-art-a7be0ae5de5c4ce7a15d76430d2840e6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a7be0ae5de5c4ce7a15d76430d2840e62025-02-03T06:05:07ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/928587928587Periodic Problems of Difference Equations and Ergodic TheoryB. A. Biletskyi0A. A. Boichuk1A. A. Pokutnyi2Department of Inductive Modeling and Control Glushkov, Institute of Cybernetics NAS Ukraine, No. 40 Glushkov Avenue, Kyiv 03680, UkraineLaboratory of boundary value problems of differential equations theory, Institute of Mathematics of NAS of Ukraine, No. 3 Tereshenkivska Street, Kyiv 01601, UkraineLaboratory of boundary value problems of differential equations theory, Institute of Mathematics of NAS of Ukraine, No. 3 Tereshenkivska Street, Kyiv 01601, UkraineThe necessary and sufficient conditions for solvability of the family of difference equations with periodic boundary condition were obtained using the notion of relative spectrum of linear bounded operator in the Banach space and the ergodic theorem. It is shown that when the condition of existence is satisfied, then such periodic solutions are built using the formula for the generalized inverse operator to the linear limited one.http://dx.doi.org/10.1155/2011/928587 |
| spellingShingle | B. A. Biletskyi A. A. Boichuk A. A. Pokutnyi Periodic Problems of Difference Equations and Ergodic Theory Abstract and Applied Analysis |
| title | Periodic Problems of Difference Equations and Ergodic Theory |
| title_full | Periodic Problems of Difference Equations and Ergodic Theory |
| title_fullStr | Periodic Problems of Difference Equations and Ergodic Theory |
| title_full_unstemmed | Periodic Problems of Difference Equations and Ergodic Theory |
| title_short | Periodic Problems of Difference Equations and Ergodic Theory |
| title_sort | periodic problems of difference equations and ergodic theory |
| url | http://dx.doi.org/10.1155/2011/928587 |
| work_keys_str_mv | AT babiletskyi periodicproblemsofdifferenceequationsandergodictheory AT aaboichuk periodicproblemsofdifferenceequationsandergodictheory AT aapokutnyi periodicproblemsofdifferenceequationsandergodictheory |