Local invariance via comparison functions
| dc.contributor.author | Carja, Ovidiu | |
| dc.contributor.author | Necula, Mihai | |
| dc.contributor.author | Vrabie, Ioan I. | |
| dc.date.accessioned | 2021-04-19T12:59:40Z | |
| dc.date.available | 2021-04-19T12:59:40Z | |
| dc.date.issued | 2004-04-06 | |
| dc.description.abstract | We consider the ordinary differential equation u'(t) = ƒ(t, u(t)), where ƒ : [a, b] x D → ℝn is a given function, while D is an open subset in ℝn. We prove that, if K ⊂ D is locally closed and there exists a comparison function ω : [a, b] x ℝ+ → ℝ such that limh↓0 inf 1/ h [d(ξ + hƒ(t, ξ); K) - d(ξ; K)] ≤ ω(t, d(ξ; K)) for each (t, ξ) ∈ [a, b] x D, then K is locally invariant with respect to ƒ. We show further that, under some natural extra condition, the converse statement is also true. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 14 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Cârjă, O., Necula, M., & Vrabie, I. I. (2004). Local invariance via comparison functions. <i>Electronic Journal of Differential Equations, 2004</i>(50), pp. 1-14. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13387 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Viable domain | |
| dc.subject | Local invariant subset | |
| dc.subject | Exterior tangency condition | |
| dc.subject | Comparison property | |
| dc.subject | Lipschitz retract | |
| dc.title | Local invariance via comparison functions | |
| dc.type | Article |