Ma, Ruyun; Lu, Yanqiong; Chen, Tianlan Existence of one-signed solutions of discrete second-order periodic boundary value problems. (English) Zbl 1232.39017 Abstr. Appl. Anal. 2012, Article ID 437912, 13 p. (2012). Summary: We prove the existence of one-signed periodic solutions of second-order nonlinear difference equation on a finite discrete segment with periodic boundary conditions by combining some properties of Green’s function with the fixed-point theorem in cones. Cited in 5 Documents MSC: 39A23 Periodic solutions of difference equations 39A12 Discrete version of topics in analysis 39A10 Additive difference equations Keywords:one-signed periodic solutions; second-order nonlinear difference equation; fixed-point theorem; cones PDFBibTeX XMLCite \textit{R. Ma} et al., Abstr. Appl. Anal. 2012, Article ID 437912, 13 p. (2012; Zbl 1232.39017) Full Text: DOI References: [1] F. M. Atici and G. S. Guseinov, “Positive periodic solutions for nonlinear difference equations with periodic coefficients,” Journal of Mathematical Analysis and Applications, vol. 232, no. 1, pp. 166-182, 1999. · Zbl 0923.39010 · doi:10.1006/jmaa.1998.6257 [2] F. M. Atici and A. Cabada, “Existence and uniqueness results for discrete second-order periodic boundary value problems,” Computers & Mathematics with Applications, vol. 45, no. 6-9, pp. 1417-1427, 2003. · Zbl 1057.39008 · doi:10.1016/S0898-1221(03)00097-X [3] F. M. Atici, A. Cabada, and V. Otero-Espinar, “Criteria for existence and nonexistence of positive solutions to a discrete periodic boundary value problem,” Journal of Difference Equations and Applications, vol. 9, no. 9, pp. 765-775, 2003. · Zbl 1056.39016 · doi:10.1080/1023619021000053566 [4] R. Ma and H. Ma, “Positive solutions for nonlinear discrete periodic boundary value problems,” Computers & Mathematics with Applications, vol. 59, no. 1, pp. 136-141, 2010. · Zbl 1197.39006 · doi:10.1016/j.camwa.2009.07.071 [5] T. He and Y. Xu, “Positive solutions for nonlinear discrete second-order boundary value problems with parameter dependence,” Journal of Mathematical Analysis and Applications, vol. 379, no. 2, pp. 627-636, 2011. · Zbl 1260.39020 · doi:10.1016/j.jmaa.2011.01.047 [6] P. J. Torres, “Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem,” Journal of Differential Equations, vol. 190, no. 2, pp. 643-662, 2003. · Zbl 1032.34040 · doi:10.1016/S0022-0396(02)00152-3 [7] W. G. Kelley and A. C. Peterson, Difference Equations-An Introduction with Applications, Academic Press, San Diego, Calif, USA, 2nd edition, 2001. · Zbl 0970.39001 [8] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985. · Zbl 0559.47040 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.