View More View Less
  • 1 Oriental Science and Technology College, Hunan Agricultural University, Changsha 410128, P. R. China
  • | 2 Guangdong Construction Vocational Technology Institute, Guangzhou 510450, P. R. China
  • | 3 Packaging Engineering Institute, Jinan University, Zhuhai 519070, P. R. China
Restricted access

Abstract

By using the critical point theory, the existence of periodic solutions to second order nonlinear p-Laplacian difference equations is obtained. The main approach used is a variational technique and the saddle point theorem. The problem is to solve the existence of periodic solutions of second order nonlinear p-Laplacian difference equations.

  • [1] Agarwal, R. P. 1992 Difference Equations and Inequalities: Theory, Methods and Applications Marcel Dekker New York.

  • [2] Agarwal, R. P., Perera, K., O’Regan, D. 2004 Multiple positive solutions of singular and nonsingular discrete problems via variational methods Nonlinear Anal. 58 6973 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [3] Agarwal, R. P., Perera, K., O’Regan, D. 2005 Multiple positive solutions of singular discrete p-Laplacian problems via variational methods Adv. Difference Equ. 2005 9399 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [4] Ahlbrandt, C. D. 1994 Dominant and recessive solutions of symmetric three term recurrences J. Differential Equations 107 238258 .

  • [5] Anderson, D. R., Avery, R. I., Henderson, J. 2006 Existence of solutions for a one dimensional p-Laplacian on time-scales J. Difference Equ. Appl. 10 889896 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [6] Avery, R. I., Henderson, J. 2004 Existence of three positive pseudo-symmetric solutions for a one dimensional discrete p-Laplacian J. Difference Equ. Appl. 10 529539 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [7] Avery, R. I., Henderson, J. 2004 Existence of three positive pseudo-symmetric solutions for a one dimensional discrete p-Laplacian J. Difference Equ. Appl. 10 529539 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [8] Cecchi, M., Marini, M., Villari, G. 1989 On the monotonicity property for a certain class of second order differential equations J. Differential Equations 82 1527 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [9] Chen, P., Fang, H. 2007 Existence of periodic and subharmonic solutions for second-order p-Laplacian difference equations Adv. Difference Equ. 2007 19 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [10] Guo, D. J. 1985 Nonlinear Functional Analysis Shandong Scientific Press Jinan.

  • [11] Guo, Z. M., Yu, J. S. 2004 Applications of critical point theory to difference equations Fields Institute Communications 42 187200.

  • [12] Guo, Z. M., Yu, J. S. 2003 The existence of periodic and subharmonic solutions for second-order superlinear difference equations Sci. China Math. 46 506515.

    • Search Google Scholar
    • Export Citation
  • [13] Guo, Z. M., Yu, J. S. 2003 The existence of periodic and subharmonic solutions of subquadratic second order difference equations J. London Math. Soc. 68 419430 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [14] He, Z. 2003 On the existence of positive solutions of p-Laplacian difference equations J. Comput. Appl. Math. 161 193201 .

  • [15] Jiang, D., Chu, J., O’Regan, D., Agarwal, R. P. 2004 Positive solutions for continuous and discrete boundary value problems to the one-dimension p-Laplacian Math. Inequal. Appl. 7 523534.

    • Search Google Scholar
    • Export Citation
  • [16] Kocic, V. L., Ladas, G. 1993 Global Behavior of Nonlinear Difference Equations of Higher Order with Application Kluwer Academic Publishers Boston.

    • Search Google Scholar
    • Export Citation
  • [17] Li, Y., Lu, L. 2006 Existence of positive solutions of p-Laplacian difference equations Appl. Math. Lett. 19 10191023 .

  • [18] Liu, Y., Ge, W. G. 2003 Twin positive solutions of boundary value problems for finite difference equations with p-Laplacian operator J. Math. Appl. 278 551561 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [19] Mawhin, J., Willem, M. 1989 Critical Point Theory and Hamiltonian Systems Springer New York.

  • [20] Mickens, R. E. 1990 Difference Equations: Theory and Application Van Nostrand Reinhold New York.

  • [21] Pankov, A., Zakharchenko, N. 2001 On some discrete variational problems Acta Appl. Math. 65 295303 .

  • [22] Rabinowitz, P. H., Minimax Methods in Critical Point Theory with Applications to Differential Equations, Amer. Math. Soc. (Providence, RI, New York, 1986).

    • Search Google Scholar
    • Export Citation
  • [23] Smets, D., Willem, M. 1997 Solitary waves with prescribed speed on infinite lattices J. Funct. Anal. 149 266275 .

  • [24] Tian, Y., Ge, W. G. 2008 The existence of solutions for a second-order discrete Neumann problem with a p-Laplacian J. Appl. Math. Comput. 26 333340 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [25] Tian, Y., Ge, W. G. 2007 Existence results for discrete Sturm–Liouville problem via variational methods J. Difference Equ. Appl. 13 467478 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [26] Yu, J. S. 2009 The minimal period problem for the classical forced pendulum equation J. Differential Equations 247 672684 .

  • [27] Yu, J. S., Long, Y. H., Guo, Z. M. 2004 Subharmonic solutions with prescribed minimal period of a discrete forced pendulum equation J. Dynam. Differential Equations 16 575586 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [28] Zhou, Z., Yu, J. S., Chen, Y. M. 2010 Periodic solutions of a 2nth-order nonlinear difference equation Sci. China Math. 53 4150 .

Acta Mathematica Hungarica
P.O. Box 127
HU–1364 Budapest
Phone: (36 1) 483 8305
Fax: (36 1) 483 8333
E-mail: acta@renyi.mta.hu

  • Impact Factor (2019): 0.588
  • Scimago Journal Rank (2019): 0.489
  • SJR Hirsch-Index (2019): 38
  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

For subscription options, please visit the website of Springer Nature

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Jun 2021 0 0 0
Jul 2021 0 0 0
Aug 2021 0 0 0
Sep 2021 0 0 0
Oct 2021 0 0 0
Nov 2021 0 0 0
Dec 2021 0 0 0