Abstract
The existence of solutions for boundary value problems for a nonlinear discrete system involving the p-Laplacian is investigated. The approach is based on critical point theory.
Similar content being viewed by others
References
D. Bai, Y. Xu: Nontrivial solutions of boundary value problems of second-order difference equations. J. Math. Anal. Appl. 326 (2007), 297–302.
G. Bonanno, P. Candito: Nonlinear difference equations investigated via critical points methods. Nonlinear Anal., Theory Methods Appl. 70 (2009), 3180–3186.
G. Bonanno, P. Candito: Infinitely many solutions for a class of discrete non-linear boundary value problems. Appl. Anal. 88 (2009), 605–616.
P. Candito, N. Giovannelli: Multiple solutions for a discrete boundary value problem involving the p-Laplacian. Comput. Math. Appl. 56 (2008), 959–964.
Z.M. Guo, J. S. Yu: Existence of periodic and subharmonic solutions for second-order superlinear difference equations. Sci. China Ser. A 46 (2003), 506–515.
Z.M. Guo, J. S. Yu: The existence of periodic and subharmonic solutions to subquadratic second order difference equations. J. Lond. Math. Soc., II. Ser. 68 (2003), 419–430.
J. Kuang: Applied Inequalities. Shandong Science and Technology Press, Jinan City, 2004. (In Chinese.)
W.D. Lu: Variational Methods in Differential Equations. Scientific Publishing House in China, 2002.
J. Ma, C. L. Tang: Periodic solutions for some nonautonomous second order systems. J. Math. Anal. Appl. 275 (2002), 482–494.
J. Mawhin, M. Willem: Critical Point Theory and Hamiltonian Systems. Springer-Verlag, New York, 1989.
P.H. Rabinowitz: Minimax Methods in Critical Point Theory with Application to Differential Equations. Reg. Conf. Ser. Math, 65. Am. Math. Soc., Provindence, 1986.
C.-L. Tang, X.-P. Wu: Notes on periodic solutions of subquadratic second order systems. J. Math. Anal. Appl. 285 (2003), 8–16.
J.F. Wu, X.P. Wu: Existence of nontrivial periodic solutions for a class of superquadratic second-order Hamiltonian systems. J. Southwest Univ. (Natural Science Edition) 30 (2008), 26–31.
X.-P. Wu, C.-L. Tang: Periodic solution of a class of non-autonomous second order systems. J. Math. Anal. Appl. 236 (1999), 227–235.
Y.-F. Xue, C.-L. Tang: Multiple periodic solutions for superquadratic second-order discrete Hamiltonian systems. Appl. Math. Comput. 196 (2008), 494–500.
Y.-F. Xue, C.-L. Tang: Existence of a periodic solution for subquadratic second-order discrete Hamiltonian system. Nonlinear Anal., Theory Methods Appl. 67 (2007), 2072–2080.
X. Zhang, X. Tang: Existence of nontrivial solutions for boundary value problems of second-order discrete systems. Math. Slovaca 61 (2011), 769–778.
F. Zhao, X. Wu: Periodic solutions for a class of nonautonomous second order systems. J. Math. Anal. Appl. 296 (2004), 422–434.
Z. Zhou, J.-S. Yu, Z.-M. Guo: Periodic solutions of higher-dimensional discrete systems. Proc. R. Soc. Edinb., Sect. A, Math. 134 (2004), 1013–1022.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by the Graduate degree thesis Innovation Foundation of Central South University (No. 3960-71131100014) and the Outstanding Doctor degree thesis Implantation Foundation of Central South University (No. 2008yb032) and partially supported by the NNSF (No. 10771215) of China.
Rights and permissions
About this article
Cite this article
Zhang, X., Tang, X. Existence of solutions for a nonlinear discrete system involving the p-Laplacian. Appl Math 57, 11–30 (2012). https://doi.org/10.1007/s10492-012-0002-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10492-012-0002-2