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A generalization of the three-dimensional Bernfeld–Haddock conjecture and its proof

✍ Scribed by Qiyuan Zhou; Wentao Wang; Qiyi Fan

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
558 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

Consider the following system of delay differential equations

where r 1 , r 2 and r 3 are positive constants, F , G ∈ C (R 1 ), and F is nondecreasing on R 1 . These systems have important practical applications and also are a three-dimensional generalization of the Bernfeld-Haddock conjecture. In this paper, by using comparative technique, we obtain the asymptotic behavior of solutions that each bounded solution of the systems tends to a constant vector under a desirable condition.

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The essential spectrum of a model proble
The essential spectrum of a model problem in 2-dimensional magnetohydrodynamics: a proof of a conjecture by J. Descloux and G. Geymonat
✍ M. Faierman; R. Mennicken; M. Möller 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 254 KB

## Abstract Descloux and Geymonat considered a model problem for plasma in a toroidal configuration and conjectured that the essential spectrum has an explicitly given band structure. Here we prove this conjecture by employing an operator matrix representation of the problem. (© 2004 WILEY‐VCH Verl