Existence of unstable manifolds for a certain class of delay differential equations
We prove a theorem for unstable manifolds in a differential equation with a state-dependent delay. Although the equation cannot be formally linearized, we find an associated linear delay equation whose dynamics are qualitatively similar near the unstable manifold. Our proof relies upon estimates of...
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| Format: | Article |
| Language: | English |
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Texas State University
2002-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2002/32/abstr.html |
| _version_ | 1818392292969414656 |
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| author | Hari P. Krishnan |
| author_facet | Hari P. Krishnan |
| author_sort | Hari P. Krishnan |
| collection | DOAJ |
| description | We prove a theorem for unstable manifolds in a differential equation with a state-dependent delay. Although the equation cannot be formally linearized, we find an associated linear delay equation whose dynamics are qualitatively similar near the unstable manifold. Our proof relies upon estimates of the derivative of a trajectory on the unstable manifold near equilibrium. |
| first_indexed | 2024-12-14T05:27:06Z |
| format | Article |
| id | doaj.art-ddfb54d38afe4bf387fb6556aa128df9 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T05:27:06Z |
| publishDate | 2002-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-ddfb54d38afe4bf387fb6556aa128df92022-12-21T23:15:28ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912002-04-01200232113Existence of unstable manifolds for a certain class of delay differential equationsHari P. KrishnanWe prove a theorem for unstable manifolds in a differential equation with a state-dependent delay. Although the equation cannot be formally linearized, we find an associated linear delay equation whose dynamics are qualitatively similar near the unstable manifold. Our proof relies upon estimates of the derivative of a trajectory on the unstable manifold near equilibrium.http://ejde.math.txstate.edu/Volumes/2002/32/abstr.htmlinvariant manifolds, functional differential equations. |
| spellingShingle | Hari P. Krishnan Existence of unstable manifolds for a certain class of delay differential equations Electronic Journal of Differential Equations invariant manifolds, functional differential equations. |
| title | Existence of unstable manifolds for a certain class of delay differential equations |
| title_full | Existence of unstable manifolds for a certain class of delay differential equations |
| title_fullStr | Existence of unstable manifolds for a certain class of delay differential equations |
| title_full_unstemmed | Existence of unstable manifolds for a certain class of delay differential equations |
| title_short | Existence of unstable manifolds for a certain class of delay differential equations |
| title_sort | existence of unstable manifolds for a certain class of delay differential equations |
| topic | invariant manifolds, functional differential equations. |
| url | http://ejde.math.txstate.edu/Volumes/2002/32/abstr.html |
| work_keys_str_mv | AT haripkrishnan existenceofunstablemanifoldsforacertainclassofdelaydifferentialequations |