Abstract
In this paper we are concerned with the study of the existence and multiplicity of connecting orbits for a singular planar Newtonian system \({\ddot{q} + V_q(t, q) = 0}\) with a periodic strong force V q (t, q), an infinitely deep well of Gordon's type at one point and two stationary points at which a potential V (t, q) achieves a strict global maximum. To this end we minimize the corresponding actiön functional over the classes of functions in the Sobolev space \({W^{1, 2}_{\rm loc}(\mathbb{R}, \mathbb{R}^2)}\) that turn a given number of times around the singularity.
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Acknowledgments
This research was supported by Grant of National Science Centre (Poland) no. 2011/03/B/ST1/04533.
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To Prof. Kazimierz Gęba on the occasion of his 80th birthday
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Izydorek, M., Janczewska, J. Connecting orbits for a periodically forced singular planar Newtonian system. J. Fixed Point Theory Appl. 12, 59–67 (2012). https://doi.org/10.1007/s11784-012-0093-0
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DOI: https://doi.org/10.1007/s11784-012-0093-0