Solutions of the generalized Lennard-Jones system |
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Authors: | Bowen Liu Yiming Long Chongchun Zeng |
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Institution: | 1. Chern Institute of Mathematics, Nankai University, Tianjin 300071, P. R. China;
2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China;
3. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA |
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Abstract: | In this paper, we study solution structures of the following generalized Lennard-Jones system in Rn,
with 0 < α < β. Considering periodic solutions with zero angular momentum, we prove that the corresponding problem degenerates to 1-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions. |
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Keywords: | Generalized Lennard-Jones system mountain pass solutions periodic solutions quasiperiodic solutions asymptotic solutions |
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