Existence of solutions in cones to delayed higher-order diff erential equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F22%3APU143920" target="_blank" >RIV/00216305:26110/22:PU143920 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0893965921001221" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0893965921001221</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aml.2022.108014" target="_blank" >10.1016/j.aml.2022.108014</a>

Result language
angličtina
Original language name
Existence of solutions in cones to delayed higher-order diff erential equations
Original language description
An n-th order delayed differential equation y^{(n)}(t) = f(t, y_t, y′_t, . . . , y^{(n−1)}_t) is considered, where y_t(θ) = y(t + θ), θ ∈ [−τ, 0], τ > 0, if t → ∞. A criterion is formulated guaranteeing the existence of a solution y = y(t) in a cone 0 < (−1)^{i−1}y^{(i−1)}(t) < (−1)^{i−1}φ^{(i−1)}(t), i = 1, . . . , n where φ is an n-times continuously diff erentiable function such that 0 < (−1)^iφ^{(i)}(t), i = 0, . . . , n. The proof is based on a similar result proved first for a system of delayed differential equations equivalent in a sense. Particular linear cases are considered and an open problem is formulated as well.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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