Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory
We provide sufficient conditions for the existence of periodic solutions of the polynomial third order differential system x.=-y+εP(x,y,z)+h1(t), y.=x+εQ(x,y,z)+h2(t), and z.=az+εR(x,y,z)+h3(t), where P, Q, and R are polynomials in the variables x, y, and z of degree n, hi(t)=hi(t+2π) with i=1,2...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/263837 |
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| _version_ | 1832551541827960832 |
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| author | Amar Makhlouf Lilia Bousbiat |
| author_facet | Amar Makhlouf Lilia Bousbiat |
| author_sort | Amar Makhlouf |
| collection | DOAJ |
| description | We provide sufficient conditions for the existence of periodic solutions of the polynomial third order differential system x.=-y+εP(x,y,z)+h1(t), y.=x+εQ(x,y,z)+h2(t), and z.=az+εR(x,y,z)+h3(t), where P, Q, and R are polynomials in the variables x, y, and z of degree n, hi(t)=hi(t+2π) with i=1,2,3 being periodic functions, a is a real number, and ε is a small parameter. |
| format | Article |
| id | doaj-art-7463031eb11140618bc28747f47837b8 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-7463031eb11140618bc28747f47837b82025-02-03T06:01:11ZengWileyInternational Journal of Differential Equations1687-96431687-96512015-01-01201510.1155/2015/263837263837Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging TheoryAmar Makhlouf0Lilia Bousbiat1Laboratory LMA, Department of Mathematics, University of Annaba, Elhadjar, 23 Annaba, AlgeriaLaboratory LMA, Department of Mathematics, University of Annaba, Elhadjar, 23 Annaba, AlgeriaWe provide sufficient conditions for the existence of periodic solutions of the polynomial third order differential system x.=-y+εP(x,y,z)+h1(t), y.=x+εQ(x,y,z)+h2(t), and z.=az+εR(x,y,z)+h3(t), where P, Q, and R are polynomials in the variables x, y, and z of degree n, hi(t)=hi(t+2π) with i=1,2,3 being periodic functions, a is a real number, and ε is a small parameter.http://dx.doi.org/10.1155/2015/263837 |
| spellingShingle | Amar Makhlouf Lilia Bousbiat Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory International Journal of Differential Equations |
| title | Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory |
| title_full | Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory |
| title_fullStr | Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory |
| title_full_unstemmed | Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory |
| title_short | Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory |
| title_sort | periodic solutions of some polynomial differential systems in dimension 3 via averaging theory |
| url | http://dx.doi.org/10.1155/2015/263837 |
| work_keys_str_mv | AT amarmakhlouf periodicsolutionsofsomepolynomialdifferentialsystemsindimension3viaaveragingtheory AT liliabousbiat periodicsolutionsofsomepolynomialdifferentialsystemsindimension3viaaveragingtheory |