On forced dynamical systems with a singularity of repulsive type. (English) Zbl 0708.34041

The existence of periodic solutions of the system \(-\ddot x=\nabla F(x)+h(t),\) where F is a potential with a singularity in zero of repulsive type (like for instance, the electrostatic potential between two charges of the same sign), satisfying also the condition: lim F(x)\(=\infty\) as \(x\to 0\), is discussed. There are given results representing conditions on h sufficient for the existence and nonexistence of T-periodic solutions. These results seem to be important since the collection of all of them permits us to established conditions being “not far away” from certain, almost full, characterization of discussed systems, from that point of view.
Reviewer: A.Pelczar


37-XX Dynamical systems and ergodic theory
34C25 Periodic solutions to ordinary differential equations
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