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Asymptotic behaviour of comparable skew‐product semiflows with applications
Author(s) -
Cao Feng,
Gyllenberg Mats,
Wang Yi
Publication year - 2011
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdq056
Subject(s) - mathematics , monotone polygon , skew , ordinary differential equation , product (mathematics) , limit (mathematics) , pure mathematics , mathematical analysis , differential equation , geometry , computer science , telecommunications
The (almost) 1‐cover lifting property of omega‐limit sets is established for non‐monotone skew‐product semiflows, which are comparable with the uniformly stable and eventually strongly monotone skew‐product semiflows. These results are then applied to study the asymptotic behaviour of solutions to the non‐monotone comparable systems of ordinary differential equations, reaction–diffusion systems, differential systems with time delays and semilinear parabolic equations.