Abstract
The 1-covering property of omega limit sets is established for monotone and uniformly stable skew-product semiflows with a minimal base flow. Then the convergence result for monotone and subhomogeneous semiflows is applied to obtain the asymptotic recurrence of solutions to a linear recurrent nonhomogeneous ordinary differential system and a nonlinear recurrent reaction-diffusion equation.
Mathematics Subject Classification (2010): Primary 37B55, 37C65; Secondary 34D23, 35K57
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Acknowledgements
Wang’s research is supported in part by the NSF of China (grant # 10801066), the FRFCU (grants # lzujbky-2011-47 and # lzujbky-2012-k26). and the FRFPM of Lanzhou University (grant # LZULL200802). Zhao’s research is supported in part by the NSERC of Canada.
Received 3/5/2009; Accepted 6/1/2010
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Wang, Y., Zhao, XQ. (2013). Global Convergence in Monotone and Uniformly Stable Recurrent Skew-Product Semiflows. In: Mallet-Paret, J., Wu, J., Yi, Y., Zhu, H. (eds) Infinite Dimensional Dynamical Systems. Fields Institute Communications, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4523-4_15
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