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International Journal of Differential Equations
Volume 2013 (2013), Article ID 728149, 6 pages
Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs
Department of Mathematics, BITS Pilani, Pilani, Rajasthan 333031, India
Received 30 April 2013; Accepted 23 June 2013
Academic Editor: Yuji Liu
Copyright © 2013 Mandeep Singh and Amit K. Verma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- C. P. Gupta and S. I. Trofimchuk, “Existence of a solution of a three-point boundary value problem and the spectral radius of a related linear operator,” Nonlinear Analysis: Theory, Methods & Applications, vol. 34, no. 4, pp. 489–507, 1998.
- Y. Liu, “Existence of three solutions to a non-homogeneous multi-point BVP of second order differential equations,” Turkish Journal of Mathematics, vol. 35, no. 1, pp. 55–86, 2011.
- R. Ma and N. Castaneda, “Existence of solutions of nonlinear -point boundary-value problems,” Journal of Mathematical Analysis and Applications, vol. 256, no. 2, pp. 556–567, 2001.
- Z. Zhang and J. Wang, “The upper and lower solution method for a class of singular nonlinear second order three-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 147, no. 1, pp. 41–52, 2002.
- Y. Liu, “A note on the existence of positive solutions of one-dimensional -Laplacian boundary value problems,” Applications of Mathematics, vol. 55, no. 3, pp. 241–264, 2010.
- J. R. L. Webb, “Existence of positive solutions for a thermostat model,” Nonlinear Analysis: Real World Applications, vol. 13, no. 2, pp. 923–938, 2012.
- Y. Zou, Q. Hu, and R. Zhang, “On numerical studies of multi-point boundary value problem and its fold bifurcation,” Applied Mathematics and Computation, vol. 185, no. 1, pp. 527–537, 2007.
- E. Picard, “Sur lapplication des metodes dapproximations succesives a letude de certains equations differentielles ordinaires,” Journal de Mathmatiques Pures et Appliques, vol. 9, pp. 217–271, 1893.
- G. S. Dragoni, “II problema dei valori ai limiti studiato in grande per le equazioni differenziali del secondo ordine,” Mathematische Annalen, vol. 105, no. 1, pp. 133–143, 1931.
- A. Cabada, P. Habets, and S. Lois, “Monotone method for the Neumann problem with lower and upper solutions in the reverse order,” Applied Mathematics and Computation, vol. 117, no. 1, pp. 1–14, 2001.
- P. Omari and M. Trombetta, “Remarks on the lower and upper solutions method for second- and third-order periodic boundary value problems,” Applied Mathematics and Computation, vol. 50, no. 1, pp. 1–21, 1992.
- A. K. Verma, “The monotone iterative method and zeros of Bessel functions for nonlinear singular derivative dependent BVP in the presence of upper and lower solutions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 14, pp. 4709–4717, 2011.
- M. Cherpion, C. de Coster, and P. Habets, “A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions,” Applied Mathematics and Computation, vol. 123, no. 1, pp. 75–91, 2001.
- X. Xian, D. O'Regan, and S. Jingxian, “Multiplicity results for three-point boundary value problems with a non-well-ordered upper and lower solution condition,” Mathematical and Computer Modelling, vol. 45, no. 1-2, pp. 189–200, 2007.
- F. Li, M. Jia, X. Liu, C. Li, and G. Li, “Existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 8, pp. 2381–2388, 2008.
- A. Cabada, J. Cid, and B. Maquez-Villamarin, “Computation of Green’s functions for boundary value problems with Mathematica,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 1919–1936, 2012.