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Higher order semipositone multi-point boundary value problems on time scales. (English) Zbl 1198.34193
Summary: The authors obtain some existence criteria for positive solutions of a higher order semipositone multi-point boundary value problem on a time scale. Applications to some special problems are also discussed. This work extends and complements many results in the literature on this topic.
MSC:
34N05Dynamic equations on time scales or measure chains
34B18Positive solutions of nonlinear boundary value problems for ODE
References:
[1]Hilger, S.: Analysis on measure chains–a unified approach to continuous and discrete calculus, Results math. 18, 18-56 (1990) · Zbl 0722.39001
[2]Bohner, M.; Peterson, A.: Dynamic equations on time scales, an introduction with applications, (2001)
[3], Advances in dynamic equations on time scales (2003)
[4]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 · doi:10.1080/10236190410001731416
[5]Han, W.; Jin, Z.; Kang, S.: Existence of positive solutions of nonlinear m-point BVP for an increasing homeomorphism and positive homomorphism on time scales, J. comput. Appl. math. 233, 188-196 (2009) · Zbl 1179.34107 · doi:10.1016/j.cam.2009.07.009
[6]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 · doi:emis:journals/EJDE/Volumes/2003/82/abstr.html
[7]Kong, L.; Kong, Q.: Positive solutions for nonlinear m-point boundary value problems on a measure chain, J. difference equ. Appl. 9, 615-627 (2003) · Zbl 1037.34015 · doi:10.1080/10236100309487539
[8]Sang, Y.; Su, H.; Xu, F.: Positive solutions of nonlinear m-point BVP for an increasing homeomorphism and homomorphism with sign changing nonlinearity on time scales, Comput. math. Appl. 58, 216-226 (2009) · Zbl 1215.34120 · doi:10.1016/j.camwa.2009.03.106
[9]Sun, H.: Triple positive solutions for p-Laplacian m-point boundary value problem on time scales, Comput. math. Appl. 58, 1736-1741 (2009) · Zbl 1197.34180 · doi:10.1016/j.camwa.2009.07.083
[10]Zhu, Y.; Zhu, J.: The multiple positive solutions for p-Laplacian multipoint BVP with sign changing nonlinearity on time scales, J. math. Anal. appl. 344, 616-626 (2008) · Zbl 1145.34016 · doi:10.1016/j.jmaa.2008.02.032
[11]A. Dogan, J.R. Graef, L. Kong, Higher order singular multi-point boundary value problems on time scales (submitted for publication). · Zbl 1223.34122 · doi:10.1017/S0013091509001643
[12]Aris, R.: Introduction to the analysis of chemical reactors, (1965)
[13]Agarwal, R. P.; Grace, S. R.; O’regan, D.: Semipositone higher-order differential equations, Appl. math. Lett. 17, 201-207 (2004) · Zbl 1072.34020 · doi:10.1016/S0893-9659(04)90033-X
[14]Anuradha, V.; Hai, D. D.; Shivaji, R.: Existence results for superlinear semipositone bvp’s, Proc. amer. Math. soc. 124, 757-763 (1996) · Zbl 0857.34032 · doi:10.1090/S0002-9939-96-03256-X
[15]Graef, J. R.; Kong, L.: Positive solutions for third order semipositone boundary value problems, Appl. math. Lett. 22, 1154-1160 (2009) · Zbl 1173.34313 · doi:10.1016/j.aml.2008.11.008
[16]Lan, K. Q.: Positive solutions of semi-positone Hammerstein integral equations and applications, Commun. pure appl. Anal. 6, 441-451 (2007) · Zbl 1134.45005 · doi:10.3934/cpaa.2007.6.441
[17]Ma, R.: Existence of positive solutions for superlinear semipositone m-point boundary value problems, Proc. edinb. Math. soc. 46, 279-292 (2003) · Zbl 1069.34036 · doi:10.1017/S0013091502000391 · doi:http://journals.cambridge.org/bin/bladerunner?REQUNIQ=1087480707&REQSESS=3723236&118000REQEVENT=&REQINT1=163425&REQAUTH=0
[18]Zhang, X.; Liu, L.; Wu, Y.: Positive solutions of nonresonance semipositone singular Dirichlet boundary value problems, Nonlinear anal. 68, 97-108 (2008) · Zbl 1135.34016 · doi:10.1016/j.na.2006.10.034
[19]Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones, (1988)