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Existence of periodic solutions for semilinear reaction diffusion systems

✍ Scribed by Norimichi Hirano; Sławomir Rybicki

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
264 KB
Volume
59
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we consider the existence of periodic solutions of reaction diffusion systems by using S 1 -degree theory due to Dylawerski et al., see Jodel et al. (Ann. Pol. Math. 41 (1991) 243).

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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 ever