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Multiple homoclinic orbits for autonomous, singular potentials

  • Ugo Bessi (a1)

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

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

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

9 R. 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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