PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2012 | 10 | 6 | 1920-1927
Tytuł artykułu

Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a conservative second order Hamiltonian system $$\ddot q + \nabla V(q) = 0$$ in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
6
Strony
1920-1927
Opis fizyczny
Daty
wydano
2012-12-01
online
2012-10-12
Twórcy
  • Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233, Gdańsk, Poland, janczewska@mif.pg.gda.pl
Bibliografia
  • [1] Bertotti M.L., Jeanjean L., Multiplicity of homoclinic solutions for singular second-order conservative systems, Proc. Roy. Soc. Edinburgh Sect. A, 1996, 126(6), 1169–1180 http://dx.doi.org/10.1017/S0308210500023349[Crossref]
  • [2] Bolotin S., Variational criteria for nonintegrability and chaos in Hamiltonian systems, In: Hamiltonian Mechanics, Torun, 28 June–2 July, 1993, NATO Adv. Sci. Inst. Ser. B Phys., 331, Plenum, New York, 1994, 173–179
  • [3] Borges M.J., Heteroclinic and homoclinic solutions for a singular Hamiltonian system, European J. Appl. Math., 2006, 17(1), 1–32 http://dx.doi.org/10.1017/S0956792506006516[Crossref]
  • [4] Caldiroli P., Jeanjean L., Homoclinics and heteroclinics for a class of conservative singular Hamiltonian systems, J. Differential Equations, 1997, 136(1), 76–114 http://dx.doi.org/10.1006/jdeq.1996.3230[Crossref]
  • [5] Caldiroli P., Nolasco M., Multiple homoclinic solutions for a class of autonomous singular systems in ℝ2, Ann. Inst. H.Poincaré Anal. Non Linéaire, 1998, 15(1), 113–125 http://dx.doi.org/10.1016/S0294-1449(99)80022-5[Crossref]
  • [6] Gordon W.B., Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc., 1975, 204, 113–135 http://dx.doi.org/10.1090/S0002-9947-1975-0377983-1[Crossref]
  • [7] Izydorek M., Janczewska J., Homoclinic solutions for a class of the second order Hamiltonian systems, J. Differential Equations, 2005, 219(2), 375–389 http://dx.doi.org/10.1016/j.jde.2005.06.029[Crossref]
  • [8] Izydorek M., Janczewska J., Heteroclinic solutions for a class of the second order Hamiltonian systems, J. Differential Equations, 2007, 238(2), 381–393 http://dx.doi.org/10.1016/j.jde.2007.03.013[Crossref]
  • [9] Janczewska J., The existence and multiplicity of heteroclinic and homoclinic orbits for a class of singular Hamiltonian systems in ℝ2, Boll. Unione Mat. Ital., 2010, 3(3), 471–491
  • [10] Rabinowitz P.H., Periodic and heteroclinic orbits for a periodic Hamiltonian system, Ann. Inst. H.Poincaré Anal. Non Linéaire, 1989, 6(5), 331–346
  • [11] Rabinowitz P.H., Homoclinics for an almost periodically forced singular Hamiltonian system, Topol. Methods Nonlinear Anal., 1995, 6(1), 49–66
  • [12] Rabinowitz P.H., Multibump solutions for an almost periodically forced singular Hamiltonian system, Electron. J. Differential Equations, 1995, #12
  • [13] Rabinowitz P.H., Homoclinics for a singular Hamiltonian system, In: Geometric Analysis and the Calculus of Variations, International Press, Cambridge, 1996, 267–296
  • [14] Tanaka K., Homoclinic orbits for a singular second order Hamiltonian system, Ann. Inst. H.Poincaré Anal. Non Linéaire, 1990, 7(5), 427–438
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0096-5
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.