Graef, John R.; Kong, Lingju Positive solutions for third order semipositone boundary value problems. (English) Zbl 1173.34313 Appl. Math. Lett. 22, No. 8, 1154-1160 (2009). Summary: We obtain some sufficient conditions for the existence of positive solutions of a third order semipositone boundary value problem with a multi-point boundary condition. Applications of our results to some special problems are also discussed. Cited in 25 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:positive solutions; semipositone boundary value problems; multi-point boundary condition PDF BibTeX XML Cite \textit{J. R. Graef} and \textit{L. Kong}, Appl. Math. Lett. 22, No. 8, 1154--1160 (2009; Zbl 1173.34313) Full Text: DOI OpenURL References: [1] Anderson, D.R.; Davis, J.M., Multiple solutions and eigenvalues for third-order right focal boundary value problems, J. math. anal. appl., 267, 135-157, (2002) · Zbl 1003.34021 [2] Clark, S.L.; Henderson, J., Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations, Proc. amer. math. soc., 134, 3363-3372, (2006) · Zbl 1120.34010 [3] Du., Z.; Liu, W.; Lin, X., Multiple solutions to a three-point boundary value problem for higher-order ordinary differential equations, J. math. anal. appl., 335, 1207-1218, (2007) · Zbl 1133.34011 [4] Eloe, P.W.; Ahmad, B., Positive solutions of a nonlinear \(n\)th order boundary value problem with nonlocal conditions, Appl. math. lett., 18, 521-527, (2005) · Zbl 1074.34022 [5] Graef, J.R.; Kong, L.; Yang, B., Existence of solutions for a higher order multi-point boundary value problem, Result. math., 53, 77-101, (2009) · Zbl 1173.34008 [6] Graef, J.R.; Yang, B., Positive solutions of a third order nonlinear boundary value problem, Discrete contin. dynam. syst. S, 1, 89-97, (2008) · Zbl 1153.34014 [7] Henderson, J.; Ntouyas, S.K., Positive solutions for systems of \(n\)th order three-point nonlocal boundary value problems, Electron J. qual. theory diff. equ., 18, 12, (2007), (electronic) · Zbl 1182.34029 [8] Aris, R., Introduction to the analysis of chemical reactors, (1965), Prentice Hall New Jersey [9] Agarwal, R.P.; Grace, S.R.; O’regan, D., Semipositone higher-order differential equations, Appl. math. lett., 17, 201-207, (2004) · Zbl 1072.34020 [10] 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 [11] Lan, K.Q., Positive solutions of semi-positone Hammerstein integral equations and applications, Comm. pure appl. anal., 6, 441-451, (2007) · Zbl 1134.45005 [12] Lan, K.Q., Multiple positive solutions of semi-positone sturm – liouville boundary value problems, Bull. London math. soc., 38, 283-293, (2006) · Zbl 1094.34014 [13] Ma, R., Positive solutions for semipositone \((k, n - k)\) conjugate boundary value problem, J. math. anal. anal., 252, 220-229, (2000) · Zbl 0979.34012 [14] Ma, R., Existence of positive solutions for superlinear semipositone \(m\)-point boundary value problems, Proc. Edinburgh math. soc., 46, 279-292, (2003) · Zbl 1069.34036 [15] 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 [16] Guo, D.; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press Orlanda · Zbl 0661.47045 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.