Chang, Yong-Kui; Li, Wan-Tong Existence results for second-order dynamic inclusion with \(m\)-point boundary value conditions on time scales. (English) Zbl 1154.34310 Appl. Math. Lett. 20, No. 8, 885-891 (2007). The authors investigate the existence of solutions of the \(m\)-point boundary problem for the second-order dynamic inclusion on a time scale \(\mathbb{T}\) \[ \begin{aligned} y^{\triangle\nabla}(t)\in F(y(t)),\qquad t\in[0,b]_{\mathbb{T}},\\ y^{\triangle}(0)=\sum_{i=1}^{m-2}a_{i}y^{\triangle}(\zeta_i), \quad y(b)=\sum_{i=1}^{m-2}b_{i}y(\zeta_i). \end{aligned} \] They use a fixed point theorem of Sadovskii and a continuous selection theorem for lower semi-continuous multi-valued maps. Reviewer: Ladislav Adamec (Brno) Cited in 8 Documents MSC: 34A60 Ordinary differential inclusions 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 39A10 Additive difference equations Keywords:Dynamic inclusions; Time scales; Boundary value; Fixed point; Lower semi-continuous multi-valued maps PDFBibTeX XMLCite \textit{Y.-K. Chang} and \textit{W.-T. Li}, Appl. Math. Lett. 20, No. 8, 885--891 (2007; Zbl 1154.34310) Full Text: DOI References: [1] Agarwal, R. P.; O’Regan, D., Nonlinear boundary value problems on time scales, Nonlinear Anal., 44, 527-535 (2001) · Zbl 0995.34016 [2] Agarwal, R. P.; Bohner, M.; Li, W.-T., (Nonoscillation and Oscillation Theory for Functional Differential Equations. Nonoscillation and Oscillation Theory for Functional Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics, vol. 267 (2004), Marcel Dekker: Marcel Dekker New York) [3] Banas, J.; Goebel, K., Measure of Noncompactness in Banach Spaces (1980), Marcel Dekker: Marcel Dekker New York · Zbl 0441.47056 [4] Bohner, M.; Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (2001), Birkhäuser: Birkhäuser Boston · Zbl 0978.39001 [5] Deimling, K., Multivalued Differential Equations (1992), De Gruyter: De Gruyter Berlin · Zbl 0760.34002 [6] Erbe, L. H.; Peterson, A., Green’s functions and comparison theorems for differential equations on measure chains, Dyn. Contin. Discrete Impuls. Syst., 6, 121-138 (1999) · Zbl 0938.34027 [7] Erbe, L. H.; Peterson, A., Positive solutions for a nonlinear differential equations on a measure chain, Math. Comput. Modelling, 32, 571-585 (2000) · Zbl 0963.34020 [8] Henderson, J., Double solutions of impulsive dynamic boundary value problems on a time scales, J. Differ. Eqns. Appl., 8, 345-356 (2002) · Zbl 1003.39019 [9] Li, W. T.; Sun, H. R., Multiple positive solutions for nonlinear dynamical systems on a measure chain, J. Comput. Appl. Math., 162, 2, 421-430 (2004) · Zbl 1045.39007 [10] Merdivenci Atici, F.; Biles, D. C., First order dynamic inclusions on time scales, J. Math. Anal. Appl., 292, 222-237 (2004) · Zbl 1064.34009 [11] Sadovskii, B. N., On a fixed point principle, Funct. Anal. Appl., 1, 74-76 (1967) · Zbl 0165.49102 [12] Sun, H. R.; Li, W. T., Positive solutions for nonlinear three-point boundary value problems on time scales, J. Math. Anal. Appl., 299, 2, 508-524 (2004) · Zbl 1070.34029 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.