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Rotating periodic solutions for second‐order dynamical systems with singularities of repulsive type
Author(s) -
Chang Xiaojun,
Li Yong
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4223
Subject(s) - gravitational singularity , mathematics , singularity , type (biology) , order (exchange) , constant (computer programming) , mathematical physics , coincidence , zero (linguistics) , mathematical analysis , dynamical systems theory , matrix (chemical analysis) , pure mathematics , physics , quantum mechanics , medicine , ecology , linguistics , philosophy , alternative medicine , materials science , finance , pathology , computer science , economics , composite material , biology , programming language
In this paper, we study the following second‐order dynamical system:u′ ′+ c u ′ + ∇ g ( u ) = e ( t ) ,where c ⩾0 is a constant, g ∈ C 1 ( R n ∖ { 0 } , R ) ( n ⩾ 2 ) and e ∈ C ( R , R n ) . 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 ) = Q u ( t ), ∀ t ∈ R with T > 0 and Q an orthogonal matrix under the assumption of Landesman–Lazer type. Copyright © 2016 John Wiley & Sons, Ltd.