Rotating periodic solutions for second‐order dynamical systems with singularities of repulsive type

In this paper, we study the following second‐order dynamical system: u′′+cu′+∇g(u)=e(t), where c⩾0 is a constant, g∈C1(Rn∖{0},R)(n⩾2) and e∈C(R,Rn). When g admits a singularity at zero of repulsive type without the restriction of strong force condition, we apply the coincidence degree theory to prov...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2017-05, Vol.40 (8), p.3092-3099
Main Authors: Chang, Xiaojun, Li, Yong
Format: Article
Language:English
Subjects:
coincidence degree theory
Dynamical systems
repulsive force
rotating periodic solutions
second‐order dynamical systems
Singularity (mathematics)
weak singularity
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Summary:In this paper, we study the following second‐order dynamical system: u′′+cu′+∇g(u)=e(t), where c⩾0 is a constant, g∈C1(Rn∖{0},R)(n⩾2) and e∈C(R,Rn). When g admits a singularity at zero of repulsive type without the restriction of strong force condition, we apply the coincidence degree theory to prove that the system admits nonplanar collisionless rotating periodic solutions taking the form u(t + T) = Qu(t), ∀t∈R with T > 0 and Q an orthogonal matrix under the assumption of Landesman–Lazer type. Copyright © 2016 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4223