Abstract
In this paper, we investigate the existence of positive solutions for singular third-order nonhomogeneous boundary value problems. By using a fixed point theorem of cone expansion-compression type due to Krasnosel’skii, we establish various results on the existence or nonexistence of single and multiple positive solutions to the singular boundary problems in the explicit intervals for the nonhomogeneous term. An example is also given to illustrate some of the main results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, D.: Multiple positive solutions for a three-point boundary value problem. Math. Comput. Model. 27, 49–57 (1998)
Anderson, D.: Green’s function for a third-order generalized right focal problem. J. Math. Anal. Appl. 288, 1–14 (2003)
Anderson, D., Davis, J.M.: Multiple solutions and eigenvalues for third-order right focal boundary value problems. J. Math. Anal. Appl. 267, 135–157 (2002)
Bai, Z., Fei, X.: Existence of triple positive solutions for a third order generalized right focal problem. Math. Inequal. Appl. 9, 437–444 (2006)
Boucherif, A., Al-Malki, N.: Nonlinear three-point third order boundary value problems. Appl. Math. Comput. 190, 1168–1177 (2007)
Sun, Y.: Positive solutions of singular third-order three-point boundary value problem. J. Math. Anal. Appl. 306, 589–603 (2005)
Yao, Q.: Positive solutions of singular third-order three-point boundary value problems. J. Math. Anal. Appl. 354, 207–212 (2009)
Graef, J.R., Yang, B.: Multiple positive solutions to a three point third order boundary value problem. Discrete Contin. Dyn. Syst. (Suppl.) 1–8 (2005)
Grossinho, M.R., Minhos, F.M.: Existence result for some third order separated boundary value problems. Nonlinear Anal. 47, 2407–2418 (2001)
Guo, L., Sun, J., Zhao, Y.: Existence of positive solution for nonlinear third-order three-point boundary value problem. Nonlinear Anal. 68(10), 3151–3158 (2008)
Ma, R.: Positive solutions for a second order three-point boundary-value problems. Appl. Math. Lett. 14, 1–5 (2001)
Sun, Y.: Positive solutions for third-order three-point nonhomogeneous boundary value problems. Appl. Math. Lett. 22, 45–51 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by NSFC (10871206).
Rights and permissions
About this article
Cite this article
Liu, Z., Chen, H. & Liu, C. Positive solutions for singular third-order nonhomogeneous boundary value problems. J. Appl. Math. Comput. 38, 161–172 (2012). https://doi.org/10.1007/s12190-010-0470-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-010-0470-z