He, Tieshan; Yang, Wei; Yang, Fengjian Sign-changing solutions for discrete second-order three-point boundary value problems. (English) Zbl 1188.39004 Discrete Dyn. Nat. Soc. 2010, Article ID 705387, 14 p. (2010). Summary: We consider the second-order three-point discrete boundary value problem. By using the topological degree theory and the fixed point index theory, we provide sufficient conditions for the existence of sign-changing solutions, positive solutions, and negative solutions. As an application, an example is given to demonstrate our main results. Cited in 5 Documents MSC: 39A12 Discrete version of topics in analysis 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations Keywords:second-order three-point discrete boundary value problem; topological degree theory; fixed point index theory; sign-changing solutions; positive solutions; negative solutions PDFBibTeX XMLCite \textit{T. He} et al., Discrete Dyn. Nat. Soc. 2010, Article ID 705387, 14 p. (2010; Zbl 1188.39004) Full Text: DOI EuDML References: [1] Monographs and Textbooks in Pure and Applied Mathematics 228 pp xvi+971– (2000) [2] pp xii+417– (1999) [3] DOI: 10.1016/j.na.2003.11.012 · Zbl 1070.39005 · doi:10.1016/j.na.2003.11.012 [4] DOI: 10.1016/j.jde.2006.08.011 · Zbl 1112.39011 · doi:10.1016/j.jde.2006.08.011 [5] DOI: 10.1016/j.na.2008.04.021 · Zbl 1166.39006 · doi:10.1016/j.na.2008.04.021 [6] DOI: 10.1016/j.jmaa.2007.07.011 · Zbl 1132.39011 · doi:10.1016/j.jmaa.2007.07.011 [7] DOI: 10.1016/j.jmaa.2006.02.091 · Zbl 1113.39018 · doi:10.1016/j.jmaa.2006.02.091 [8] DOI: 10.1016/j.amc.2005.12.018 · Zbl 1113.39023 · doi:10.1016/j.amc.2005.12.018 [9] DOI: 10.1016/j.camwa.2007.08.033 · Zbl 1147.39008 · doi:10.1016/j.camwa.2007.08.033 [10] DOI: 10.1016/j.na.2004.07.023 · Zbl 1069.34019 · doi:10.1016/j.na.2004.07.023 [11] DOI: 10.1016/j.na.2007.05.030 · Zbl 1152.34006 · doi:10.1016/j.na.2007.05.030 [12] DOI: 10.1016/j.jmaa.2005.04.008 · Zbl 1094.34012 · doi:10.1016/j.jmaa.2005.04.008 [13] (1995) [14] Notes and Reports in Mathematics in Science and Engineering 5 pp viii+275– (1988) [15] (2001) [16] Grundlehren der Mathematischen Wissenschaften 263 pp xix+409– (1984) [17] DOI: 10.1016/j.jmaa.2003.09.061 · Zbl 1054.34025 · doi:10.1016/j.jmaa.2003.09.061 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.