Periodic solutions of nonlinear second-order difference equations
<p/> <p>We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form <it>y</it>(<it>t</it> + 2) + <it>by</it> (<it>t</it> + 1) + <it>cy</it>(<it>t</it>)...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2005-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2005/718682 |
| _version_ | 1818558784760446976 |
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| author | Etheridge Debra Lynn Rodriguez Jesús |
| author_facet | Etheridge Debra Lynn Rodriguez Jesús |
| author_sort | Etheridge Debra Lynn |
| collection | DOAJ |
| description | <p/> <p>We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form <it>y</it>(<it>t</it> + 2) + <it>by</it> (<it>t</it> + 1) + <it>cy</it>(<it>t</it>) = <it>f</it> (<it>y</it>(<it>t</it>)), where <it>f</it>: ℝ → ℝ and <it>β</it> > 0 is continuous. In our main result we assume that <it>f</it> exhibits sublinear growth and that there is a constant <it>uf</it> (<it>u</it>) > 0 such that |<it>u</it>| ≥ <it>β</it> whenever <it>c</it> = 1. For such an equation we prove that if <it>N</it> is an odd integer larger than one, then there exists at least one <it>N</it>-periodic solution unless all of the following conditions are simultaneously satisfied: |<it>b</it>| < 2, <it>N across</it><sup>-1</sup>(-<it>b</it>/2), and <it>π</it> is an even multiple of <it>c</it> ≠ 0.</p> |
| first_indexed | 2024-12-14T00:16:48Z |
| format | Article |
| id | doaj.art-32155bef0a6e45c9822db902ad5bad80 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T00:16:48Z |
| publishDate | 2005-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-32155bef0a6e45c9822db902ad5bad802022-12-21T23:25:29ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472005-01-0120052718682Periodic solutions of nonlinear second-order difference equationsEtheridge Debra LynnRodriguez Jesús<p/> <p>We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form <it>y</it>(<it>t</it> + 2) + <it>by</it> (<it>t</it> + 1) + <it>cy</it>(<it>t</it>) = <it>f</it> (<it>y</it>(<it>t</it>)), where <it>f</it>: ℝ → ℝ and <it>β</it> > 0 is continuous. In our main result we assume that <it>f</it> exhibits sublinear growth and that there is a constant <it>uf</it> (<it>u</it>) > 0 such that |<it>u</it>| ≥ <it>β</it> whenever <it>c</it> = 1. For such an equation we prove that if <it>N</it> is an odd integer larger than one, then there exists at least one <it>N</it>-periodic solution unless all of the following conditions are simultaneously satisfied: |<it>b</it>| < 2, <it>N across</it><sup>-1</sup>(-<it>b</it>/2), and <it>π</it> is an even multiple of <it>c</it> ≠ 0.</p>http://www.advancesindifferenceequations.com/content/2005/718682 |
| spellingShingle | Etheridge Debra Lynn Rodriguez Jesús Periodic solutions of nonlinear second-order difference equations Advances in Difference Equations |
| title | Periodic solutions of nonlinear second-order difference equations |
| title_full | Periodic solutions of nonlinear second-order difference equations |
| title_fullStr | Periodic solutions of nonlinear second-order difference equations |
| title_full_unstemmed | Periodic solutions of nonlinear second-order difference equations |
| title_short | Periodic solutions of nonlinear second-order difference equations |
| title_sort | periodic solutions of nonlinear second order difference equations |
| url | http://www.advancesindifferenceequations.com/content/2005/718682 |
| work_keys_str_mv | AT etheridgedebralynn periodicsolutionsofnonlinearsecondorderdifferenceequations AT rodriguezjes250s periodicsolutionsofnonlinearsecondorderdifferenceequations |