AM  Vol.3 No.9 , September 2012
Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem
ABSTRACT
By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .

Cite this paper
A. Guezane-Lakoud and L. Zenkoufi, "Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem," Applied Mathematics, Vol. 3 No. 9, 2012, pp. 1008-1013. doi: 10.4236/am.2012.39149.
References
[1]   D. Anderson and R. Avery, “Multiple Positive Solutions to Third-Order Discrete Focal Boundary Value Problem,” Acta Mathematicae Applicatae Sinica, Vol. 19, No. 1, 2003, pp. 117-122. doi:10.1007/s10255-003-0087-1

[2]   D. R. Anderson, “Green’s Function for a Third-Order Generalized Right Focal Problem,” Journal of Mathematical Analysis and Applications, Vol. 288, No. 1, 2003, pp. 1-14. doi:10.1016/S0022-247X(03)00132-X

[3]   A. Guezane-Lakoud and L. Zenkoufi, “Positive Solution of a Three-Point Nonlinear Boundary Value Problem for Second Order Differential Equations,” International Journal of Applied Mathematics and Statistics, Vol. 20, 2011, pp. 38-46.

[4]   A. Guezane-Lakoud and S. Kelaiaia, “Solvability of a Three-Point Nonlinear Noundary-Value Problem,” Electronic Journal of Differential Equations, Vol. 2010, No. 139, 2010, pp. 1-9.

[5]   A. Guezane-Lakoud, S. Kelaiaia, A. M. Eid, “A Positive Solution for a Non-local Boundary Value Problem,” International Journal of Open Problems in Computer Science and Mathematics, Vol. 4, No. 1, 2011, pp. 36-43.

[6]   J. R. Graef and Bo Yang, “Existence and Nonexistence of Positive Solutions of a Nonlinear Third Order Boundary Value Problem,” Electronic Journal of Qualitative Theory of Differential Equations, No. 9, 2008, pp. 1-13.

[7]   J. R. Graef and B. Yang, “Positive Solutions of a Nonlinear Third Order Eigenvalue Problem,” Dynamic Systems & Applications, Vol. 15, 2006, pp. 97-110.

[8]   S. Li, “Positive Solutions of Nonlinear Singular ThirdOrder Two-Point Boundary Value Problem,” Journal of Mathematical Analysis and Applications, Vol. 323, No. 1, 2006, pp. 413-425. doi:10.1016/j.jmaa.2005.10.037

[9]   B. Hopkins and N. Kosmatov, “Third-Order Boundary Value Problems with Sign-Changing Solutions,” Nonlinear Analysis, Vol. 67, No. 1, 2007, pp. 126-137. doi:10.1016/j.na.2006.05.003

[10]   L. J. Guo, J. P. Sun and Y. H. Zhao, “Existence of Positive Solutions for Nonlinear Third-Order Three-Point Boundary Value Problem,” Nonlinear Analysis, Vol. 68, No. 10, 2008, pp. 3151-3158. doi:10.1016/j.na.2007.03.008

[11]   Y. Sun, “Positive Solutions of Singular Third-Order ThreePoint Boundary Value Problem,” Journal of Mathematical Analysis and Applications, Vol. 306, No. 2, 2005, pp. 589-603. doi:10.1016/j.jmaa.2004.10.029

[12]   K. Deimling, “Nonlinear Functional Analysis,” Springer, Berlin, 1985. doi:10.1007/978-3-662-00547-7

[13]   D. Guo and V. Lakshmikantham, “Nonlinear Problems in Abstract Cones,” Academic Press, San Diego, 1988.

 
 
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