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Higher-order three-point boundary value problem on time scales. (English) Zbl 1165.39300
Summary: We consider a higher-order three-point boundary value problem on time scales. We study the existence of solutions of a non-eigenvalue problem and of at least one positive solution of an eigenvalue problem. Later we establish the criteria for the existence of at least two positive solutions of a non-eigenvalue problem. Examples are also included to illustrate our results.

MSC:
39A10 Additive difference equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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[1] Bohner, M.; Peterson, A., ()
[2] Bohner, M.; Peterson, A., Advances in dynamic equations on time scales, (2003), Birkhäuser Boston · Zbl 1025.34001
[3] Anderson, D.R., Solutions to second order three-point problems on time scales, J. difference equ. appl., 8, 673-688, (2002) · Zbl 1021.34011
[4] Anderson, D.R., Nonlinear triple-point problems on time scales, Electron. J. differential equations, 47, 1-12, (2004) · Zbl 1053.34014
[5] DaCunha, J.J.; Davis, J.M.; Singh, P.K., Existence results for singular three-point boundary value problems on time scales, J. math. anal. appl., 295, 378-391, (2004) · Zbl 1069.34012
[6] Karaca, I.Y., Positive solutions to nonlinear three point boundary value problems on time scales, Panamer. math. J., 17, 33-49, (2007) · Zbl 1203.34154
[7] Kaufmann, E.R., Positive solutions of a three-point boundary value problem on a time scale, Electron. J. differential equations, 82, 1-11, (2003) · Zbl 1047.34015
[8] Kaufmann, E.R.; Raffoul, Y., Eigenvalue problems of a three-point boundary value problem on a time scale, Electron. J. qualitative theory differential equations, 2, 1-10, (2004) · Zbl 1081.34023
[9] Luo, H.; Ma, Q., Positive solutions to a generalized second-order three-point boundary-value problem on time scales, Electron. J. differential equations, 17, 1-14, (2005) · Zbl 1075.34014
[10] Ma, R., Positive solutions of a nonlinear three-point boundary value problem, Electron. J. differential equations, 34, 1-8, (1999)
[11] Peterson, A.C.; Raffoul, Y.N.; Tisdell, C.C., Three point boundary value problems on time scales, J. difference equ. appl., 10, 843-849, (2004) · Zbl 1078.39016
[12] Sun, H.R.; Li, W.T., Positive solutions for nonlinear three-point boundary value problems on time scales, J. math. anal. appl., 299, 508-524, (2004) · Zbl 1070.34029
[13] Anderson, D.R.; Avery, R.I., An even-order three-point boundary value problem on time scales, J. math. anal. appl., 291, 514-525, (2004) · Zbl 1056.34013
[14] Henderson, J., Multiple solutions for 2mth order sturm – liouville boundary value problems on a measure chain, J. difference equ. appl., 6, 417-429, (2000) · Zbl 0965.39008
[15] Chyan, C.J., Eigenvalue intervals for 2mth order sturm – liouville boundary value problems, J. difference equ. appl., 8, 403-413, (2002) · Zbl 1033.34022
[16] Henderson, J.; Prasad, K.R., Comparison of eigenvalues for lidstone boundary value problems on a measure chain, Comput. math. appl., 38, 55-62, (1999) · Zbl 1010.34079
[17] Cetin, E.; Topal, S.G., Higher order boundary value problems on time scales, J. math. anal. appl., 334, 876-888, (2007) · Zbl 1124.34009
[18] Liu, B., Positive solutions of a nonlinear three-point boundary value problem, Comput. math. appl., 44, 201-211, (2002) · Zbl 1008.34014
[19] Ma, R.; Raffoul, Y.N., Positive solutions of three-point nonlinear discrete second order boundary value problem, J. difference equ. appl., 10, 129-138, (2004) · Zbl 1056.39024
[20] Krasnosel’skii, M.A., Positive solutions of operator equations, (1964), Noordhoff Groningen · Zbl 0121.10604
[21] Avery, R.I.; Henderson, J., Two positive fixed points of nonlinear operators on ordered Banach spaces, Comm. appl. nonlinear anal., 8, 27-36, (2001) · Zbl 1014.47025
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