Abstract
In this paper, we are concerned with periodic solutions, quasi-periodic solutions and unbounded solutions for radially symmetric systems with singularities at resonance, which are 2π-periodic in time. The method is based on the qualitative analysis of Poincaré map with action-angle variables. The existence of infinitely many periodic and quasi-periodic solutions or unbounded motions depends on the oscillatory properties of a certain function.
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Liu, Q., Torres, P.J. & Qian, D. Periodic, quasi-periodic and unbounded solutions of radially symmetric systems with repulsive singularities at resonance. Nonlinear Differ. Equ. Appl. 22, 1115–1142 (2015). https://doi.org/10.1007/s00030-015-0316-3
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DOI: https://doi.org/10.1007/s00030-015-0316-3