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Convergence to Periodic Solutions in Periodic Quasimonotone Reaction–Diffusion Systems

✍ Scribed by Yi Wang

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
144 KB
Volume
268
Category
Article
ISSN
0022-247X

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✦ Synopsis

The author studies the periodic time-dependent quasimonotone reactiondiffusion systems

in a proper Banach space satisfying (i) ∂F i /∂u j ≥ 0 for all 1 ≤ i = j ≤ n; (ii) F t x u is periodic in t of period τ > 0; and (iii) F i t x αu ≥ αF i t x u for all α ∈ 0 1 and i = 1 2 n. It is proved that every solution of such a system converges to a periodic solution. The same result also holds if we replace (iii) by (iii) F t x u is analytic and every τ-periodic solution is Liapounov stable.  2002 Elsevier Science (USA)

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