Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations
<p/> <p>We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general <it>n</it>th problem in time scales with linear dependence on the <it>i</it>th Δ-derivatives for <it>i</it> = 1,2,…...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2004-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2004/438603 |
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doaj-d9a91da439314253be2d35bedfc55d462020-11-25T00:15:13ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472004-01-0120044438603Existence and uniqueness of solutions of higher-order antiperiodic dynamic equationsCabada AlbertoVivero Dolores R<p/> <p>We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general <it>n</it>th problem in time scales with linear dependence on the <it>i</it>th Δ-derivatives for <it>i</it> = 1,2,…,<it>n</it>, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of the equation is defined by a function <it>f</it>(<it>t</it>,<it>x</it>) which is rd-continuous in <it>t</it> and continuous in <it>x</it> uniformly in <it>t</it>. To do that, we obtain the expression of the Green's function of a related linear operator in the space of the antiperiodic functions.</p>http://www.advancesindifferenceequations.com/content/2004/438603 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Cabada Alberto Vivero Dolores R |
| spellingShingle |
Cabada Alberto Vivero Dolores R Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations Advances in Difference Equations |
| author_facet |
Cabada Alberto Vivero Dolores R |
| author_sort |
Cabada Alberto |
| title |
Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations |
| title_short |
Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations |
| title_full |
Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations |
| title_fullStr |
Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations |
| title_full_unstemmed |
Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations |
| title_sort |
existence and uniqueness of solutions of higher-order antiperiodic dynamic equations |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1839 1687-1847 |
| publishDate |
2004-01-01 |
| description |
<p/> <p>We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general <it>n</it>th problem in time scales with linear dependence on the <it>i</it>th Δ-derivatives for <it>i</it> = 1,2,…,<it>n</it>, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of the equation is defined by a function <it>f</it>(<it>t</it>,<it>x</it>) which is rd-continuous in <it>t</it> and continuous in <it>x</it> uniformly in <it>t</it>. To do that, we obtain the expression of the Green's function of a related linear operator in the space of the antiperiodic functions.</p> |
| url |
http://www.advancesindifferenceequations.com/content/2004/438603 |
| work_keys_str_mv |
AT cabadaalberto existenceanduniquenessofsolutionsofhigherorderantiperiodicdynamicequations AT viverodoloresr existenceanduniquenessofsolutionsofhigherorderantiperiodicdynamicequations |
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