Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument
We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear ho...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/514854 |
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| _version_ | 1832567609811271680 |
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| author | Kuo-Shou Chiu |
| author_facet | Kuo-Shou Chiu |
| author_sort | Kuo-Shou Chiu |
| collection | DOAJ |
| description | We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green’s function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results. |
| format | Article |
| id | doaj-art-b0c2908dac5d416389c7ebd417b087d8 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-b0c2908dac5d416389c7ebd417b087d82025-02-03T01:01:00ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/514854514854Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant ArgumentKuo-Shou Chiu0Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, Santiago, ChileWe investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green’s function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results.http://dx.doi.org/10.1155/2014/514854 |
| spellingShingle | Kuo-Shou Chiu Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument The Scientific World Journal |
| title | Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument |
| title_full | Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument |
| title_fullStr | Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument |
| title_full_unstemmed | Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument |
| title_short | Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument |
| title_sort | periodic solutions for nonlinear integro differential systems with piecewise constant argument |
| url | http://dx.doi.org/10.1155/2014/514854 |
| work_keys_str_mv | AT kuoshouchiu periodicsolutionsfornonlinearintegrodifferentialsystemswithpiecewiseconstantargument |