Journal of Fixed Point Theory and Applications

, Volume 12, Issue 1, pp 59–67

Connecting orbits for a periodically forced singular planar Newtonian system

Open Access

DOI: 10.1007/s11784-012-0093-0

Cite this article as:
Izydorek, M. & Janczewska, J. J. Fixed Point Theory Appl. (2012) 12: 59. doi:10.1007/s11784-012-0093-0


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 Vq(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.

Mathematics Subject Classification

Primary 34C37 Secondary 49M10 


Heteroclinic orbits homoclinic orbits Newtonian systems 
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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Faculty of Applied Physics and MathematicsGdańsk University of TechnologyGdańskPoland

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