On asymptotics of oscillatory solutions to nth-order delay differential equations
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Bibliographic record
Abstract
We study bounded and decaying to zero solutions of the delay differential equation x ( n ) ( t ) + ∑ i = 1 m p i ( t ) x ( t − τ i ( t ) ) = 0 for t ∈ [ 0 , ∞ ) , t ≥ 0 , x ( ξ ) = φ ( ξ ) for ξ < 0 . Kondrat'ev and Kiguradze introduced and defined principles of asymptotic behavior for its solution in the sense of the trichotomy: oscillatory, non-oscillatory with absolute values monotonically decaying to zero or monotonically increasing to ∞. Expanding upon such studies, we estimate the oscillation amplitudes of solutions. Decay to zero is established through fast oscillation: once distances between zeros are small enough, the Grönwall inequality growth estimate implies the amplitudes decrease to zero as t → ∞ . Exact growth estimates and calculation of these distances between zeros are proposed through evaluation for the spectral radii of some compact operators associated with the Green's function for an n -point problem.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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