Abstract
The study of existence and multiplicity of solutions of differential equations possessing a variational nature is a problem of great meaning since most of them derives from mechanics and physics. In particular, this relates to Hamiltonian systems including Newtonian ones. During the past 30 years there has been a great deal of progress in the use of variational methods to find periodic, homoclinic and heteroclinic solutions of Hamiltonian systems. Hamiltonian systems with singular potentials, i.e., potentials that become infinite at a point or a larger subset of \(\mathbb{R}^{n}\), are among those of the greatest interest. Let us remark that such potentials arise in celestial mechanics. For example, the Kepler problem with
has a point singularity at \(\xi\) (\(q \in \mathbb{R}^{n}\setminus \{\xi \}\)). In physics, the gradient ∇V of the gravitational potential is called a weak force.
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Acknowledgements
The research is supported by the Grant number 2011/03/B/ST1/04533 of National Science Centre of Poland.
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Janczewska, J. (2015). Homoclinic and Heteroclinic Orbits for a Class of Singular Planar Newtonian Systems. In: Corbera, M., Cors, J., Llibre, J., Korobeinikov, A. (eds) Extended Abstracts Spring 2014. Trends in Mathematics(), vol 4. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-22129-8_7
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DOI: https://doi.org/10.1007/978-3-319-22129-8_7
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