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Homoclinics for singular strong force Lagrangian systems

Abstract

We study the existence of homoclinic solutions for a class of generalized Lagrangian systems in the plane, with a C1-smooth potential with a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin.Under a strong force condition around the singular point ξ, via minimization of an action integral, we will prove the existence of at least two geometrically distinct homoclinic solutions.

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Details

Category:
Articles
Type:
artykuły w czasopismach
Published in:
Advances in Nonlinear Analysis no. 9, pages 644 - 653,
ISSN: 2191-9496
Language:
English
Publication year:
2020
Bibliographic description:
Izydorek M., Janczewska J., Mawhin J.: Homoclinics for singular strong force Lagrangian systems// Advances in Nonlinear Analysis -Vol. 9,iss. 1 (2020), s.644-653
DOI:
Digital Object Identifier (open in new tab) 10.1515/anona-2020-0018
Bibliography: test
  1. N.S. Trudinger, An imbedding theorem for H (G, Ω) spaces, Studia Math. 50 (1974), 17-30. open in new tab
  2. J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences 74, Springer- Verlag, New York, 1989. open in new tab
  3. R.T. Rockafellar, Convex Analysis, Monographs and Textbooks in Pure and Applied Mathematics 146, Princeton University Press, Princeton, 1970.
  4. V.K. Le, On second order elliptic equations and variational inequalities with anisotropic principial operators, Topol. Meth- ods Nonlinear Anal. 44 (2014), no. 1, 41-72. open in new tab
  5. J.P. Aubin, Optima and Equilibria, Graduate Text in Mathematics 140, Springer-Verlag, Berlin, 1993. open in new tab
  6. M.A. Krasnosel'skiȋ and Ya.B. Rutickiȋ, Convex Functions and Orlicz Spaces, P. Noordho Ltd., Groningen, 1961.
  7. P.H. Rabinowitz, Homoclinics for a singular Hamiltonian system, in: Geometric Analysis and the Calculus of Variations, International Press, Cambridge, MA (1996), 267-297. open in new tab
  8. R.A. Adams and J.J.F. Fournier, Sobolev Spaces, Pure and Applied Mathematics 140, Academic Press, 2009. open in new tab
  9. W.B. Gordon, Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc. 204 (1975), 113-135. open in new tab
  10. A. Ambrosetti and V. Coti Zelati, Periodic Solutions of Singular Lagrangian Systems, Progress in Nonlinear Di erential Equations and their Applications 10, Birkhäuser Boston, Inc., Boston, MA, 1993. open in new tab
  11. I. Ekeland, Convexity Methods in Hamiltonian Mechanics, Results in Mathematics and Related Areas 19, Springer-Verlag, Berlin, 1990. open in new tab
  12. H. Hofer and E. Zehnder, Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser Advanced Texts: Basel Textbooks, Birkhäuser Verlag, Basel, 1994. open in new tab
  13. P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Di erential Equations, CBMS Reg. Conf. Ser. in Math. 65, 1986. open in new tab
  14. K. Cieliebak and E. Séré, Pseudoholomorphic curves and multiplicity of homoclinic orbits, Duke Math. J. 77 (1995), 483- 518. open in new tab
  15. V. Coti Zelati, I. Ekeland, E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann. 288 (1990), 133-160. open in new tab
  16. H. Hofer and K. Wysocki, First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems, Math. Ann. 288 (1990), 483-503. open in new tab
  17. M. Izydorek and J. Janczewska, The shadowing chain lemma for singular Hamiltonian systems involving strong forces, Cent. Eur. J. Math. 10 (2012), no. 6, 1928-1939. open in new tab
  18. J. Janczewska and J. Maksymiuk, Homoclinic orbits for a class of singular second order Hamiltonian systems in R , Cent. Eur. J. Math. 10 (2012), no. 6, 1920-1927. open in new tab
  19. M.M. Rao and Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, Inc., New York, 1991. open in new tab
  20. P.H. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), 331-346. open in new tab
  21. M. Izydorek and J. Janczewska, Heteroclinic solutions for a class of the second order Hamiltonian systems, J. Di erential Equations 238 (2007), no. 2, 381-393. Brought to you by | Instytut Matematyczny Pan open in new tab
Sources of funding:
Verified by:
Gdańsk University of Technology

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