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Existence of positive solutions for $p$-Laplacian dynamic equations with derivative on time scales. (English) Zbl 1266.35108
Summary: We consider the existence of positive solutions of nonlinear $p$-Laplacian dynamic equations with derivative on time scales. Applying the Avery-Peterson fixed point theorem, we obtain at least three positive solutions to the problem. An example is also presented to illustrate the applications of the obtained results.
##### MSC:
 35J92 Quasilinear elliptic equations with $p$-Laplacian 35B09 Positive solutions of PDE
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##### References:
 [1] S. H. Hong, “Triple positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales,” Journal of Computational and Applied Mathematics, vol. 206, no. 2, pp. 967-976, 2007. · Zbl 1120.39019 · doi:10.1016/j.cam.2006.09.002 [2] I. Yaslan, “Multiple positive solutions for nonlinear three-point boundary value problems on time scales,” Computers and Mathematics with Applications, vol. 55, no. 8, pp. 1861-1869, 2008. · Zbl 1159.34317 · doi:10.1016/j.camwa.2007.07.005 [3] P. G. Wang and Y. Wang, “Existence of positive solutions for second-order m-point boundary value problems on time scales,” Acta Mathematica Sinica, vol. 50, no. 3, pp. 701-706, 2007. · Zbl 1140.34335 [4] I. Yaslan, “Multi-point boundary value problems on time scales,” Nonlinear Dynamics and Systems Theory, vol. 10, no. 3, pp. 305-316, 2010. · Zbl 1219.34122 [5] J. P. Sun, “Twin positive solutions of nonlinear first-order boundary value problems on time scales,” Nonlinear Analysis, Theory, Methods and Applications, vol. 68, no. 6, pp. 1754-1758, 2008. · Zbl 1139.34303 · doi:10.1016/j.na.2007.01.002 [6] D. R. Anderson and I. Y. Karaca, “Higher-order three-point boundary value problem on time scales,” Computers and Mathematics with Applications, vol. 56, no. 9, pp. 2429-2443, 2008. · Zbl 1165.39300 · doi:10.1016/j.camwa.2008.05.018 [7] Y. Li and H. Zhang, “Positive periodic solutions of neutral functional differential equations with state dependent delays on time scales,” Acta Mathematica Sinica, vol. 30, no. 3, pp. 730-742, 2010. · Zbl 1240.34477 [8] Y. Tian and W. Ge, “Existence and uniqueness results for nonlinear first-order three-point boundary value problems on time scales,” Nonlinear Analysis, Theory, Methods and Applications, vol. 69, no. 9, pp. 2833-2842, 2008. · Zbl 1155.34012 · doi:10.1016/j.na.2007.08.054 [9] J. Fan, X. Zhang, and Y. Liu, “Existence of positive solutions of the m-point boundary value problem with p-Laplace operator on time scales,” Journal of Shandong University, vol. 47, no. 6, pp. 16-19, 2012 (Chinese). · Zbl 1265.34335 [10] J. Fan, X. Zhang, and Y. Liu, “Positive solutions of nonlinear m-point bound- ary value problem with p-Laplace operator on time scales,” Journal of University of Jinan, vol. 26, no. 4, pp. 415-418, 2012 (Chinese). [11] M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäauser, Boston, Mass, USA, 2003. · Zbl 1025.34001