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Han, Wei; Kang, Shugui

Multiple positive solutions of nonlinear third-order BVP for a class of \(p\)-Laplacian dynamic equations on time scales. (English) Zbl 1165.34321

Math. Comput. Modelling 49, No. 3-4, 527-535 (2009).

Cited in 14 Documents

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
39A10 Additive difference equations

Keywords:

time scales; \(p\)-Laplacian operator; third-order bvps; fixed-point index; positive solutions
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\textit{W. Han} and \textit{S. Kang}, Math. Comput. Modelling 49, No. 3--4, 527--535 (2009; Zbl 1165.34321)
Full Text: DOI

References:

[1] Agarwal, R. P.; Bohner, M.; Rehak, P., Half-linear dynamic equations, (Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th birthday (2003), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), 1-57 · Zbl 1056.34049
[2] Agarwal, R. P.; O’Regan, D., Nonlinear boundary value Problems on time scales, Nonlinear Anal., 44, 527-535 (2001) · Zbl 0995.34016
[3] Anderson, D. R.; Avery, R.; Henderson, J., Existence of solutions for a one-dimensional \(p\)-Laplacian on time scales, J. Difference Equ. Appl., 10, 889-896 (2004) · Zbl 1058.39010
[4] Anderson, D. R.; Gnseinov, G. Sh.; Hoffacker, J., Higher-order self-adjoint boundary-value problems on time scales, J. Comput. Appl. Math., 194, 309-342 (2006) · Zbl 1098.39008
[5] Atici, F. M.; Gnseinov, G. Sh., On Green’n functions and positive solutions for boundary value problems on time scales, J. Comput. Anal. Math., 141, 75-99 (2002) · Zbl 1007.34025
[6] Aulbach, B.; Neidhart, L., Integration on measure chain, (Proc. of the Sixth Int. Conf. on Difference Equations (2004), CRC: CRC BocaRaton, Fl), 239-252 · Zbl 1083.26005
[7] Bai, C. Z.; Fang, J. X., Existence of multiple positive solutions for nonlinear \(m\) point boundary value problems, J. Math. Anal. Appl., 281, 76-85 (2003) · Zbl 1030.34026
[8] Bohner, M.; Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (2001), Birkhäuser: Birkhäuser Boston, Cambridge, MA · Zbl 0978.39001
[9] Bohner, M.; Peterson, A., Advances in Dynamic Equations on Time Scales (2003), Birkhäuser: Birkhäuser Boston, Cambridge, MA · Zbl 1025.34001
[10] Erbe, L. H.; Peterson, A., Positive solutions for nonlinear differential equation on a measure chain, Math. Comput. Modelling, 32, 571-585 (2000) · Zbl 0963.34020
[11] Grossinho, M. R.; Minhós, F. M.; Santos, A. I., Existence results for a third-order ODE with nonlinear boundary conditions in presence of a sign-type Nagumo control, J. Math. Anal. Appl., 309, 271-283 (2005) · Zbl 1089.34017
[12] Guo, D. J.; Sun, J. X., Topological degree’s computation and application, J. Math. Res. Exposition, 8, 3, 469-480 (1988), (in Chinese)
[13] Hao, Z. C.; Liang, J.; Xiao, T. J., Existence results for time scale boundary value problem, J. Comput. Appl. Math., 197, 156-168 (2006) · Zbl 1107.34018
[14] He, Z. M., Triple positive solutions of boundary value problems for \(p\)-Laplacian dynamic equations on time scales, J. Math. Anal. Appl., 321, 911-920 (2006) · Zbl 1103.34012
[15] Li, S. H., Positive solutions of nonlinear singular third-order two-point boundary value problem, J. Math. Anal. Appl., 323, 413-425 (2006) · Zbl 1107.34019
[16] Ma, D.; Du, Z.; Ge, W., Existence and iteration of monotone positive solutions for multipoint boundary value problem with \(p\)-Laplacian operator, Comput. Math. Appl., 50, 729-739 (2005) · Zbl 1095.34009
[17] Ma, R. Y., Existence of solutions of nonlinear \(m\)-point boundary value problem, J. Math. Anal. Appl., 256, 556-567 (2001) · Zbl 0988.34009
[18] Mao, A. M.; Luan, S. X.; Ding, Y. H., On the existence of positive solutions for a class of singular boundary value problems, J. Math. Appl., 298, 57-72 (2004) · Zbl 1073.34019
[19] Su, H.; Wang, B.; Wei, Z., Positive solutions of four-point boundary value problems for four-order \(p\)-Laplacian dynamic equations on time scales, Electron. J. Differential Equations, 78, 1-13 (2006) · Zbl 1117.34028
[20] Su, H.; Wei, Z.; Xu, F., The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the \(p\)-Laplacian operator, J. Math. Anal. Appl., 325, 319-332 (2007) · Zbl 1108.34015
[21] Sun, H. R.; Li, W. T., Existence theory for positive solutions to one-dimensional \(p\)-Laplacian boundary value problems on time scales, J. Differential Equations, 240, 217-248 (2007) · Zbl 1139.34047
[22] Sun, H. R.; Li, W. T., Multiple positive solutions for \(p\)-Laplacian \(m\)-point boundary value problems on time scales, Appl. Math. Comput., 182, 478-491 (2006) · Zbl 1126.34019
[23] Sun, Y. P., Positive solutions of singular third-order three-point boundary value problem, J. Math. Anal. Appl., 306, 589-603 (2005) · Zbl 1074.34028
[24] Zhou, C. L.; Ma, D. X., Existence and iteration of positive solutions for a generalized right-focal boundary value problem with \(p\)-Laplacian operator, J. Math. Anal. Appl., 324, 409-424 (2006) · Zbl 1115.34029
[25] Minhós, F., On some third order nonlinear boundary value problems: Existence, location and multiplicity results, J. Math. Anal. Appl., 339-2, 1342-1353 (2008) · Zbl 1144.34009
[26] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press: Academic Press San Diego · Zbl 0661.47045
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