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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Costa, David G. and Tehrani, Hossein 2014. On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions. Journal of Mathematical Analysis and Applications, Vol. 412, Issue. 1, p. 200.


    Zhang, Ziheng Liao, Fang-Fang and Wong, Patricia J. Y. 2014. Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems. Abstract and Applied Analysis, Vol. 2014, p. 1.


    Rabinowitz, P.H. 2002.


    Zhang, Shiqing 2000. Symmetrically Homoclinic Orbits for Symmetric Hamiltonian Systems. Journal of Mathematical Analysis and Applications, Vol. 247, Issue. 2, p. 645.


    Caldiroli, Paolo and Jeanjean, Louis 1997. Homoclinics and Heteroclinics for a Class of Conservative Singular Hamiltonian Systems. Journal of Differential Equations, Vol. 136, Issue. 1, p. 76.


    Caldiroli, Paolo and De Coster, Colette 1997. Multiple Homoclinics for a Class of Singular Hamiltonian Systems. Journal of Mathematical Analysis and Applications, Vol. 211, Issue. 2, p. 556.


    Bertotti, Maria Letizia and Jeanjean, Louis 1996. Multiplicity of homoclinic solutions for singular second-order conservative systems. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 126, Issue. 06, p. 1169.


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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 124, Issue 4
  • January 1994, pp. 785-802

Multiple homoclinic orbits for autonomous, singular potentials

  • Ugo Bessi (a1)
  • DOI: http://dx.doi.org/10.1017/S0308210500028651
  • Published online: 14 November 2011
Abstract

We consider the problem

where uRn, n ≧ 2, and VC2(Rne, R) is a potential having an absolute maximum at 0 and such that V(x) → − ∞ as x → e. We prove that, under some conditions on V, this problem has at least n − 1 geometrically distinct solutions.

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1S. I. Al'ber . On periodicity problems in the calculus of variations in the large. Russian Math. Surveys 25(4) (1970), 51117.

4V. Coti Zelati , I. Ekeland and E. Seré . A variational approach to homoclinic orbits in Hamiltonian systems. Math. Ann. 288 (1990), 133160.

5V. Coti Zelati and P. H. Rabinowitz . Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. J. Amer. Math. Soc. 4 (1991), 693727.

9R. S. Palais . Homotopy theory of infinite dimensional manifolds. Topology 5 (1966), 116.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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