Previous |  Up |  Next

Article

Keywords:
critical point theory; boundary value problems; discrete systems; $p$-Laplacian; variational method
Summary:
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.
References:
[1] Bai, D., Xu, Y.: Nontrivial solutions of boundary value problems of second-order difference equations. J. Math. Anal. Appl. 326 (2007), 297-302. DOI 10.1016/j.jmaa.2006.02.091 | MR 2277783 | Zbl 1113.39018
[2] Bonanno, G., Candito, P.: Nonlinear difference equations investigated via critical points methods. Nonlinear Anal., Theory Methods Appl. 70 (2009), 3180-3186. DOI 10.1016/j.na.2008.04.021 | MR 2503063
[3] Bonanno, G., Candito, P.: Infinitely many solutions for a class of discrete non-linear boundary value problems. Appl. Anal. 88 (2009), 605-616. DOI 10.1080/00036810902942242 | MR 2541143 | Zbl 1176.39004
[4] Candito, P., Giovannelli, N.: Multiple solutions for a discrete boundary value problem involving the $p$-Laplacian. Comput. Math. Appl. 56 (2008), 959-964. DOI 10.1016/j.camwa.2008.01.025 | MR 2437868 | Zbl 1155.39301
[5] Guo, Z. M., Yu, J. S.: Existence of periodic and subharmonic solutions for second-order superlinear difference equations. Sci. China Ser. A 46 (2003), 506-515. DOI 10.1007/BF02884022 | MR 2014482 | Zbl 1215.39001
[6] Guo, Z. M., Yu, J. S.: The existence of periodic and subharmonic solutions to subquadratic second order difference equations. J. Lond. Math. Soc., II. Ser. 68 (2003), 419-430. DOI 10.1112/S0024610703004563 | MR 1994691
[7] Kuang, J.: Applied Inequalities. Shandong Science and Technology Press Jinan City (2004), Chinese.
[8] Lu, W. D.: Variational Methods in Differential Equations. Scientific Publishing House in China (2002).
[9] Ma, J., Tang, C. L.: Periodic solutions for some nonautonomous second order systems. J. Math. Anal. Appl. 275 (2002), 482-494. DOI 10.1016/S0022-247X(02)00636-4 | MR 1943760 | Zbl 1024.34036
[10] Mawhin, J., Willem, M.: Critical Point Theory and Hamiltonian Systems. Springer-Verlag New York (1989). MR 0982267 | Zbl 0676.58017
[11] Rabinowitz, P. H.: Minimax Methods in Critical Point Theory with Application to Differential Equations. Reg. Conf. Ser. Math, 65. Am. Math. Soc. Provindence (1986). MR 0845785
[12] Tang, C.-L., Wu, X.-P.: Notes on periodic solutions of subquadratic second order systems. J. Math. Anal. Appl. 285 (2003), 8-16. DOI 10.1016/S0022-247X(02)00417-1 | MR 2000135 | Zbl 1054.34075
[13] Wu, J. F., Wu, X. P.: Existence of nontrivial periodic solutions for a class of superquadratic second-order Hamiltonian systems. J. Southwest Univ. (Natural Science Edition) 30 (2008), 26-31.
[14] Wu, X.-P., Tang, C.-L.: Periodic solution of a class of non-autonomous second order systems. J. Math. Anal. Appl. 236 (1999), 227-235. DOI 10.1006/jmaa.1999.6408 | MR 1704579
[15] Xue, Y.-F., Tang, C.-L.: Multiple periodic solutions for superquadratic second-order discrete Hamiltonian systems. Appl. Math. Comput. 196 (2008), 494-500. DOI 10.1016/j.amc.2007.06.015 | MR 2388705 | Zbl 1153.39024
[16] Xue, Y.-F., Tang, C.-L.: Existence of a periodic solution for subquadratic second-order discrete Hamiltonian system. Nonlinear Anal., Theory Methods Appl. 67 (2007), 2072-2080. DOI 10.1016/j.na.2006.08.038 | MR 2331858 | Zbl 1129.39008
[17] Zhang, X., Tang, X.: Existence of nontrivial solutions for boundary value problems of second-order discrete systems. Math. Slovaca 61 (2011), 769-778. DOI 10.2478/s12175-011-0044-z | MR 2827213 | Zbl 1274.39018
[18] Zhao, F., Wu, X.: Periodic solutions for a class of nonautonomous second order systems. J. Math. Anal. Appl. 296 (2004), 422-434. DOI 10.1016/j.jmaa.2004.01.041 | MR 2075174 | Zbl 1050.34062
[19] Zhou, Z., Yu, J.-S., Guo, Z.-M.: Periodic solutions of higher-dimensional discrete systems. Proc. R. Soc. Edinb., Sect. A, Math. 134 (2004), 1013-1022. DOI 10.1017/S0308210500003607 | MR 2099576 | Zbl 1073.39010
Partner of
EuDML logo