Entire solutions in periodic lattice dynamical systems |
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Authors: | Shi-Liang Wu Zhen-Xia Shi Fei-Ying Yang |
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Institution: | 1. Department of Mathematics, Xidian University, Xi?an, Shaanxi 710071, People?s Republic of China;2. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People?s Republic of China;3. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People?s Republic of China |
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Abstract: | This paper deals with entire solutions of periodic lattice dynamical systems. Unlike homogeneous problems, the periodic equation studied here lacks symmetry between increasing and decreasing pulsating traveling fronts, which affects the construction of entire solutions. In the bistable case, the existence, uniqueness and Liapunov stability of entire solutions are proved by constructing different sub- and supersolutions. In the monostable case, the existence and asymptotic behavior of spatially periodic solutions connecting two steady states are first established. Some new types of entire solutions are then constructed by combining leftward and rightward pulsating traveling fronts with different speeds and a spatially periodic solution. Various qualitative features of the entire solutions are also investigated. |
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Keywords: | 34K05 34A34 34E05 |
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