Multiple homoclinic solutions for a class of autonomous singular systems in R2

Paolo Caldiroli; Margherita Nolasco

Annales de l'I.H.P. Analyse non linéaire (1998)

  • Volume: 15, Issue: 1, page 113-125
  • ISSN: 0294-1449

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Caldiroli, Paolo, and Nolasco, Margherita. "Multiple homoclinic solutions for a class of autonomous singular systems in R2." Annales de l'I.H.P. Analyse non linéaire 15.1 (1998): 113-125. <http://eudml.org/doc/78429>.

@article{Caldiroli1998,
author = {Caldiroli, Paolo, Nolasco, Margherita},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Hamiltonian system; homoclinic orbit; unstable equilibrium point; concentration-compactness; Ekeland principle},
language = {eng},
number = {1},
pages = {113-125},
publisher = {Gauthier-Villars},
title = {Multiple homoclinic solutions for a class of autonomous singular systems in R2},
url = {http://eudml.org/doc/78429},
volume = {15},
year = {1998},
}

TY - JOUR
AU - Caldiroli, Paolo
AU - Nolasco, Margherita
TI - Multiple homoclinic solutions for a class of autonomous singular systems in R2
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 1
SP - 113
EP - 125
LA - eng
KW - Hamiltonian system; homoclinic orbit; unstable equilibrium point; concentration-compactness; Ekeland principle
UR - http://eudml.org/doc/78429
ER -

References

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  1. [AB] A. Ambrosetti and M.L. Bertotti, Homoclinics for second order conservative systems, in Partial Differential Equations and Related Subjects, ed. M. Miranda, Pitman Research Notes in Math. Ser. (London, Pitman Press), 1992. Zbl0804.34046MR1190931
  2. [ACZ] A. Ambrosetti and V. Coti Zelati, Multiple Homoclinic Orbits for a Class of Conservative Systems, Rend. Sem. Mat. Univ. Padova, Vol. 89, 1993, pp. 177-194. Zbl0806.58018MR1229052
  3. [BC] A. Bahri and J.M. Coron, On a Nonlinear Elliptic Equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 253-294. Zbl0649.35033MR929280
  4. [BG] V. Benci and F. Giannoni, Homoclinic orbits on compact manifolds, J. Math. Anal. Appl., Vol. 157, 1991, pp. 568-576. Zbl0737.58052MR1112335
  5. [Be] U. Bessi, Multiple homoclinic orbits for autonomous singular potentials, Proc. Roy. Soc. Edinburgh Sect. A, Vol. 124, 1994, pp. 785-802. Zbl0812.58088MR1298592
  6. [B] S.V. Bolotin, Existence of homoclinic motions, Vestnik Moskov. Univ. Ser. I Mat. Mekh., Vol. 6, 1980, pp. 98-103. Zbl0549.58019MR728558
  7. [BS] B. Buffoni and E. Séré, A global condition for quasi random behavior in a class of conservative systems, Vol. XLIX, 1996, pp. 285-305. Zbl0860.58027MR1374173
  8. [C] P. Caldiroli, Existence and multiplicity of homoclinic orbits for potentials on unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A, Vol. 124, 1994, pp. 317-339. Zbl0807.34058MR1273751
  9. [CZES] V. CotiZELATI, I. EKELAND and E. SÉRÉ, A Variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann., Vol. 288, 1990, pp. 133-160. Zbl0731.34050MR1070929
  10. [CZR] V. Coti Zelati and P.H. Rabinowitz, Homoclinic orbits for second order hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc., Vol. 4, 1991, pp. 693-727. Zbl0744.34045MR1119200
  11. [G] W.B. Gordon, Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc., Vol. 204, 1975, pp. 113-135. Zbl0276.58005MR377983
  12. [J] L. Jeanjean, Existence of connecting orbits in a potential well, Dyn. Sys. Appl., Vol. 3, 1994, pp. 537-562. Zbl0817.34029MR1304132
  13. [L] P.L. Lions, The concentration-compactness principle in the calculus of variations, Rev. Mat. Iberoamericana, Vol. 1, 1985, pp. 145-201. Zbl0704.49005MR834360
  14. [R] P.H. Rabinowitz, Homoclinics for a singular Hamiltonian system in R2, Proceedings of the Workshop "Variational and Local Methods in the Study of Hamiltonian Systems", ICTP (A. Ambrosetti and G. F. Dell' Antonio, eds.), World Scientific, 1995. Zbl0951.37015MR1449412
  15. [R2] P.H. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system, Ann. Inst. H. Poincaré. Anal. Non Linéaire, Vol. 6, 1989, pp. 331-346. Zbl0701.58023MR1030854
  16. [RT] P.H. Rabinowitz and K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z., Vol. 206, 1991, pp. 473-479. Zbl0707.58022MR1095767
  17. [S] E. Séré, Homoclinic orbits on compact hypersurfaces in R2N of restricted contact type, Comm. Math. Phys., Vol. 172, 1995, pp. 293-316. Zbl0840.34046MR1350410
  18. [T] K. Tanaka, Homoclinic orbits for a singular second order Hamiltonian system, Ann. Inst. H. Poincaré. Anal. Non Linéaire, Vol. 7, 1990, pp. 427-438. Zbl0712.58026MR1138531
  19. [T2] K. Tanaka, A note on the existence of multiple homoclinic orbits for a perturbed radial potential, Nonlinear Diff. Eq. Appl., Vol. 1, 1994, pp. 149-162. Zbl0819.34032MR1273347

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