Homoclinic Orbits for Second Order Discrete Hamiltonian Systems with General Potentials

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• 作者：Huiwen Chen ; Zhimin He
• 关键词：Homoclinic solutions ; Discrete Hamiltonian systems ; Variational methods ; Variant fountain theorem ; 37J45 ; 39A12 ; 58E05 ; 70H05
• 刊名：Differential Equations and Dynamical Systems
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：23
• 期：4
• 页码：387-401
• 全文大小：497 KB
• 参考文献：1.Agarwal, R.P.: Difference Equations and Inequalities: Theory, Methods, and Applications, 2nd edn. Marcel Dekker Inc, New York (2000)
  2.Ahlbrandt, C.D., Peterson, A.C.: Discrete Hamiltonian Systems: Difference Equations, Continued Fraction and Riccati Equations. Kluwer, Dordrecht (1996)CrossRef MATH
  3.Caldiroli, P., Montecchiari, P.: Homoclinic orbits for second order Hamiltonian systems with potential changing sign. Commun. Appl. Nonlinear Anal. 1(2), 97鈥?29 (1994)MathSciNet MATH
  4.Carriao, P.C., Miyagaki, O.H.: Existence of homoclinic solutions for a class of time-dependent Hamiltonian systems. J. Math. Anal. Appl. 291, 203鈥?13 (2004)MathSciNet CrossRef
  5.Chen, H.W., He, Z.M.: Homoclinic solutions for second order discrete Hamiltonian systems with superquadratic potentials. J. Differ. Equ. Appl. 19, 1147鈥?160 (2013)CrossRef MATH
  6.Chen, H.W., He, Z.M.: Infinitely many homoclinic solutions for second-order discrete Hamiltonian systems. J. Differ. Equ. Appl. 19, 1940鈥?951 (2013)CrossRef MATH
  7.Coti Zelati, V., Rabinowitz, P.H.: Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. J. Am. Math. Soc. 4, 693鈥?27 (1991)MathSciNet CrossRef MATH
  8.Coti Zelati, V., Ekeland, I., Sere, E.: A variational approach to homoclinic orbits in Hamiltonian systems. Math. Ann. 288(1), 133鈥?60 (1990)MathSciNet CrossRef MATH
  9.Deng, X.Q., Chen, G.: Homoclinic orbits for second order discrete Hamiltonian systems with potentials changing sign. Acta Appl. Math. 103, 301鈥?14 (2008)MathSciNet CrossRef MATH
  10.Ding, Y.H.: Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems. Nonlinear Anal. 25, 1095鈥?113 (1995)MathSciNet CrossRef MATH
  11.Izydorek, M., Janczewska, J.: Homoclinic solutions for a class of the second order Hamiltonian systems. J. Differ. Equ. 219, 375鈥?89 (2005)MathSciNet CrossRef MATH
  12.Kato, T.: Perturbation Theory for Linear Operators. Springer, Berlin (1995)MATH
  13.Lin, X.Y., Tang, X.H.: Existence of infinitely homoclinic orbits in discrete Hamiltonian systems. J. Math. Anal. Appl. 373, 59鈥?2 (2011)MathSciNet CrossRef MATH
  14.Ma, M.J., Guo, Z.M.: Homoclinic orbits for second order self-adjoint difference equations. J. Math. Anal. Appl. 323(1), 513鈥?21 (2006)MathSciNet CrossRef MATH
  15.Ma, M.J., Guo, Z.M.: Homoclinic orbits and subharmonics for nonlinear second order difference equations. Nonlinear Anal. 67, 1737鈥?745 (2007)MathSciNet CrossRef MATH
  16.Omana, W., Willem, M.: Homoclinic orbits for a class of Hamiltonian systems. Differ. Int. Equ. 5, 1115鈥?120 (1992)MathSciNet MATH
  17.Paturel, E.: Multiple homoclinic orbits for a class of Hamiltonian systems. Calc. Var. Partial Differ. Equ. 12, 117鈥?43 (2001)MathSciNet CrossRef MATH
  18.Rabinowitz, P.H.: Homoclinic orbits for a class of Hamiltonian systems. Proc. R. Soc. Edinb. Sect. A 114, 33鈥?8 (1990)MathSciNet CrossRef MATH
  19.Rabinowitz, P.H., Tanaka, K.: Some results on connecting orbits for a class of Hamiltonian Systems. Math. Z. 206, 473鈥?99 (1991)MathSciNet CrossRef MATH
  20.Salvatore, A.: Homoclinic orbits for a special class of nonautonomous Hamiltonian systems. Nonlinear Anal. 30, 4849鈥?857 (1997)MathSciNet CrossRef MATH
  21.Sun, J., Chen, H., Nieto, J.J.: Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems. J. Math. Anal. Appl. 373, 20鈥?9 (2011)MathSciNet CrossRef MATH
  22.Tang, X.H., Lin, X.Y.: Existence and multiplicity of homoclinic solutions for second-order discrete Hamiltonian systems with subquadratic potential. J. Differ. Equ. Appl. 17, 1617鈥?634 (2011)MathSciNet CrossRef MATH
  23.Tang, X.H., Lin, X.Y.: Infinitely many homoclinic orbits for discrete Hamiltonian systems with subquadratic potential. J. Differ. Equ. Appl. 19, 796鈥?13 (2013)MathSciNet CrossRef MATH
  24.Tang, X.H., Lin, X.Y., Xiao, L.: Homoclinic solutions for a class of second order discrete Hamiltonian systems. J. Differ. Equ. Appl. 16, 1257鈥?273 (2010)MathSciNet CrossRef MATH
  25.Tian, Y., Ge, W.: Periodic solutions of non-autonomous second-order systems with a \(p\) -Laplacian. Nonlinear Anal. 66, 192鈥?03 (2007)MathSciNet CrossRef MATH
  26.Tian, Y., Ge, W.: Applications of variational methods to boundary value problem for impulsive differential equations. Proc. Edinb. Math. Soc. 51, 509鈥?27 (2008)MathSciNet CrossRef MATH
  27.Tian, Y., Ge, W.: Variational methods to Sturm鈥揕iouville boundary value problem for impulsive differential equations. Nonlinear Anal. 72, 277鈥?87 (2010)MathSciNet CrossRef MATH
  28.Wang, Z.Q.: Nonlinear boundary value problems with concave nonlinearities near the origin. Nonlinear Differ. Equ. Appl. (NoDEA) 8, 15鈥?3 (2001)CrossRef MATH
  29.Weidmann, J.: In: J. Sz眉cs (Trans.) Linear Operators in Hilbert Spaces. Springer, New York (1980)
  30.Willem, M.: Minimax Theorems. Birkh盲user, Boston (1996)CrossRef MATH
  31.Zhang, Q., Liu, C.: Infinitely many homoclinic solutions for second order Hamiltonian systems. Nonlinear Anal. 72, 894鈥?03 (2010)MathSciNet CrossRef MATH
  32.Zhang, X., Shi, Y.M.: Homoclinic orbits of a class of second-order difference equations. J. Math. Anal. Appl. 396, 810鈥?28 (2012)MathSciNet CrossRef MATH
  33.Zhang, Z.H., Yuan, R.: Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems. Nonlinear Anal. 71, 4125鈥?130 (2009)MathSciNet CrossRef MATH
  34.Zou, W.M.: Variant fountain theorems and their applications. Manuscr. Math. 104, 343鈥?58 (2001)CrossRef MATH
  
• 作者单位：Huiwen Chen (1)
  Zhimin He (1)
  
  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People鈥檚 Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  
• 出版者：Springer India
• ISSN：0974-6870

文摘

In this paper, we study the second order discrete Hamiltonian system $$\begin{aligned} \Delta ^2 u(n-1)-L(n)u(n)+\nabla W(n,u(n))=0, \end{aligned}$$