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Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems

Yıl 2020, , 178 - 188, 01.12.2020
https://doi.org/10.33205/cma.796813

Öz

In this paper, we consider the periodic solutions of the following non-autonomous second order
discrete Hamiltonian system
$$\Delta^{2}u(n-1)=\nabla F(n,u(n)), \quad n\in\mathbb{Z}.$$
When the nonlinear function $F(n,x)$ is like-quadratic for $x$, we obtain some existence and multiplicity results under twisting conditions by using the least action principle and a multiple critical point theorem. The methods and main ideas using in this paper are variational method and critical point theory. The twisting conditions in our results are different from that in the lituratures.

Kaynakça

  • H. Brezis, L. Nirenberg, {\it Remarks on finding critical points}, Commun. Pure Appl. Math., 1991, 44(8-9):939-963.
  • Z.M. Guo and J.S. Yu, {\it Existence of periodic and subharmonic solutions for second-order superlinear difference equations}, Sci. China Ser. A, 2003, 46(4): 506-515.
  • Z.M. Guo and J.S. Yu, {\it The existence of periodic and subharmonic solutions to subquadratic second-order difference equations}, J. Lond. Math. Soc., 2003, 68(2):419-430.
  • Z.M. Guo and J.S. Yu, {\it Periodic and subharmonic solutions for superquadratic discrete Hamiltonian systems}, Nonlinear Anal., 2003, 55(7-8):969-983.
  • W. Guan and K. Yang, {\it Existence of periodic solutions for a class of second order discrete Hamiltonian systems}, Adv. Difference Equ., 2016, (68).
  • J. Hu, {\it Existence and Multiplicity of Periodic Solutions for Second-order Discete Hamiltonian Systems}, J. Harbin Univ. Sci. Tech., 2010, 15(05):119-123.
  • J. Mawhin and M. Willem, Critical point theory and Hamiltonian systems, {\it Springer-Verlag, New York}, 1989.
  • X. H. Tang and X.Y. Zhang, {\it Periodic solutions for second-order discrete Hamiltonian systems}, J. Difference Equ. Appl, 2011, 17(10):1413-1430.
  • Y.F. Xue and C.L. Tang, {\it Existence and Multiplicity of Periodic Solutions for Second-Order Discrete Hamiltonian Systems}, J. Southwest China Normal Univ. Nat. Sci. Ed., 2006, 31(1):7-12.
  • Y.F. Xue and C.L. Tang, {\it Multiple periodic solutions for superquadratic second-order discrete Hamiltonian systems}, Appl. Math. Comput., 2008, 196(2):494-500.
  • Z. Zhou, J.S. Yu and Z.M. Guo, {\it Periodic solutions of higher-dimensional discrete systems}, Proc. Roy. Soc. Edinburgh Sect. A, 2004, 134(5):1013-1022.
Yıl 2020, , 178 - 188, 01.12.2020
https://doi.org/10.33205/cma.796813

Öz

Kaynakça

  • H. Brezis, L. Nirenberg, {\it Remarks on finding critical points}, Commun. Pure Appl. Math., 1991, 44(8-9):939-963.
  • Z.M. Guo and J.S. Yu, {\it Existence of periodic and subharmonic solutions for second-order superlinear difference equations}, Sci. China Ser. A, 2003, 46(4): 506-515.
  • Z.M. Guo and J.S. Yu, {\it The existence of periodic and subharmonic solutions to subquadratic second-order difference equations}, J. Lond. Math. Soc., 2003, 68(2):419-430.
  • Z.M. Guo and J.S. Yu, {\it Periodic and subharmonic solutions for superquadratic discrete Hamiltonian systems}, Nonlinear Anal., 2003, 55(7-8):969-983.
  • W. Guan and K. Yang, {\it Existence of periodic solutions for a class of second order discrete Hamiltonian systems}, Adv. Difference Equ., 2016, (68).
  • J. Hu, {\it Existence and Multiplicity of Periodic Solutions for Second-order Discete Hamiltonian Systems}, J. Harbin Univ. Sci. Tech., 2010, 15(05):119-123.
  • J. Mawhin and M. Willem, Critical point theory and Hamiltonian systems, {\it Springer-Verlag, New York}, 1989.
  • X. H. Tang and X.Y. Zhang, {\it Periodic solutions for second-order discrete Hamiltonian systems}, J. Difference Equ. Appl, 2011, 17(10):1413-1430.
  • Y.F. Xue and C.L. Tang, {\it Existence and Multiplicity of Periodic Solutions for Second-Order Discrete Hamiltonian Systems}, J. Southwest China Normal Univ. Nat. Sci. Ed., 2006, 31(1):7-12.
  • Y.F. Xue and C.L. Tang, {\it Multiple periodic solutions for superquadratic second-order discrete Hamiltonian systems}, Appl. Math. Comput., 2008, 196(2):494-500.
  • Z. Zhou, J.S. Yu and Z.M. Guo, {\it Periodic solutions of higher-dimensional discrete systems}, Proc. Roy. Soc. Edinburgh Sect. A, 2004, 134(5):1013-1022.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Chungen Lıu 0000-0001-7240-7377

Yuyou Zhong Bu kişi benim 0000-0002-6885-1747

Yayımlanma Tarihi 1 Aralık 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Lıu, C., & Zhong, Y. (2020). Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems. Constructive Mathematical Analysis, 3(4), 178-188. https://doi.org/10.33205/cma.796813
AMA Lıu C, Zhong Y. Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems. CMA. Aralık 2020;3(4):178-188. doi:10.33205/cma.796813
Chicago Lıu, Chungen, ve Yuyou Zhong. “Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems”. Constructive Mathematical Analysis 3, sy. 4 (Aralık 2020): 178-88. https://doi.org/10.33205/cma.796813.
EndNote Lıu C, Zhong Y (01 Aralık 2020) Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems. Constructive Mathematical Analysis 3 4 178–188.
IEEE C. Lıu ve Y. Zhong, “Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems”, CMA, c. 3, sy. 4, ss. 178–188, 2020, doi: 10.33205/cma.796813.
ISNAD Lıu, Chungen - Zhong, Yuyou. “Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems”. Constructive Mathematical Analysis 3/4 (Aralık 2020), 178-188. https://doi.org/10.33205/cma.796813.
JAMA Lıu C, Zhong Y. Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems. CMA. 2020;3:178–188.
MLA Lıu, Chungen ve Yuyou Zhong. “Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems”. Constructive Mathematical Analysis, c. 3, sy. 4, 2020, ss. 178-8, doi:10.33205/cma.796813.
Vancouver Lıu C, Zhong Y. Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems. CMA. 2020;3(4):178-8.