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,…...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2004-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2004/438603 |
| Summary: | <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> |
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| ISSN: | 1687-1839 1687-1847 |