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Original Articles

Multiplicity results for periodic solutions with prescribed minimal periods to discrete Hamiltonian systems

Pages 1499-1518 | Received 11 Jun 2009, Accepted 22 Jan 2010, Published online: 26 Feb 2010

References

  • Agarwal , R.P. 1992 . Difference Equations and Inequalities: Theory, Methods and Applications , New York : Marcel Dekker .
  • Ambrosetti , A. and Rabinowitz , P.H. 1973 . Dual variational methods in critical point theory and applications . J. Funct. Anal. , 14 : 349 – 381 .
  • Birkhoff , G.D. and Lewis , D.C. 1933 . On the periodic motion near a given periodic motion of a dynamical system . Ann. Math. Pure Appl. , 12 : 117 – 133 .
  • Chang , K.C. 1980 . Critical Point Theory and its Applications , Shanghai, China : Science and technical Press .
  • Ekeland , I. and Hofer , H. 1987 . Subhamonics for convex nonautonomous Hamiltonian systems . Commun. Pure Appl. Math. , 40 : 1 – 36 .
  • Elaydi , S. 1996 . An Introduction to Difference Equation , New York : Springer .
  • Guo , Z.M. and Yu , J.S. 2003 . The existence of the periodic and subharmonic solutions for superquadratic discrete Hamiltonian systems . Nonlinear Anal. TMA , 55 : 969 – 983 .
  • Kelly , W.G. and Peterson , A.C. 1991 . Difference Equations: An Introduction with Applications , New York : Academic Press .
  • Kocic , V.L. and Ladas , G. 1993 . Global Behavior of Nonlinear Difference Equations of Higher Order with Application , Boston : Kluwer Academic .
  • Liu , J.Q. and Wang , Z.Q. 1993 . Remarks on subharmonics with minimal periods of Hamiltonian systems . Nonlinear Anal. TMA. , 20 : 803 – 821 .
  • Long , Y. 1990 . Period solution of perturbed superquadratic Hamiltonian systems . Annalen Scola Normale Superiore di Pisa. Series 4 , 17 : 35 – 77 .
  • Mawin , J. and Willem , M. 1989 . Critical Point Theory and Hamiltonian Systems , New York : Springer-Verlag .
  • Michalek , R. and Tarantello , G. 1988 . Subharmonics solutions with prescriebed minimal period for nonautonomous Hamiltonian systems . J. Differential Equations , 72 : 28 – 55 .
  • Mickens , R.E. 1990 . Difference Equations: Theory and Application , New York : Van Nostrand Reinhold .
  • Morse , J. 1977 . Proof of generalized fixed point theorem due to G.D. Birkhoff , Lecture Notes in Mathematics Vol. 597 , 35 – 49 . New York : Springer-Verlag .
  • Rabinowitz , P.H. 1974 . “ Variational methods for nonlinear eigenvalue problems ” . In Eigenvalues of Nonlinear Problems , Edited by: Prodi , G. 141 – 195 . Rome : Edizioni Cremonese .
  • Rabinowitz , P.H. 1980 . On subharmonic solution of Hamiltonian systems . Commun. Pure Appl. Math. , 33 : 609 – 633 .
  • Rabinowitz , P.H. 1987 . Periodic solution of Hamiltonian systems . Commun. Pure Appl. Math. , 40 : 157 – 184 .
  • Sharkovsky , A.N. , Maistrenko , Y.L. and Romanenko , E.Y. 1993 . Difference Equations and Their Applications , Dordrecht : Kluwer Academic .
  • An , Tianqing . 2007 . On the minimal periodic solutions of nonconvex superlinear Hamiltonian systems . J. Math. Anal. Appl. , 329 : 1273 – 1284 .
  • Xu , Y.T. and Guo , Z.M. 2001 . Applications of a geometrical index theory to functional differential equations . Acta Math. Sinica , 44 ( 6 ) : 1027 – 1036 .
  • Xu , Y.T. and Guo , Z.M. 2001 . Applications of a Z p index theory to periodic solutions for a class of functional differential equations . J. Math. Anal. Appl. , 257 : 189 – 205 .
  • Yu , J.S. , Bin , H.H. and Guo , Z.M. 2006 . Periodic solutions for discrete convex Hamiltonian systems via Clark duality . Discrete Contin. Dyn. Syst. , 15 : 939 – 950 .
  • Zhou , Z. , Yu , J.S. and Guo , Z.M. 2005 . The existence of the periodic and subharmonics solutions to subquadratic discrete Hamiltonian systems . ANZIAM J. Aust. Math. Soc. , 47 : 89 – 102 .

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