- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 489353, 12 pages
Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation
1Faculty of Science, Alexandria University, Alexandria, Egypt
2Faculty of Science, Garyounis University, Benghazi, Libya
Received 13 October 2011; Accepted 5 December 2011
Academic Editor: István Györi
Copyright © 2012 A. M. A. El-Sayed et al. 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.
- V. A. Il'in and E. I. Moiseev, “A nonlocal boundary value problem of the first kind for the Sturm-Liouville operator in differential and difference interpretations,” Differentsial'nye Uravneniya, vol. 23, no. 7, pp. 1198–1207, 1987.
- V. A. Il'in and E. I. Moiseev, “A nonlocal boundary value problem of the second kind for the Sturm-Liouville operator,” Differentsial'nye Uravneniya, vol. 23, no. 8, pp. 1422–1431, 1987.
- Y. An, “Existence of solutions for a three-point boundary value problem at resonance,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 8, pp. 1633–1643, 2006.
- R. F. Curtain and A. J. Pritchand, Functional Analysis in Modern Applied Mathematics, Academic Press, 1977.
- P. W. Eloe and Y. Gao, “The method of quasilinearization and a three-point boundary value problem,” Journal of the Korean Mathematical Society, vol. 39, no. 2, pp. 319–330, 2002.
- A. M. A. El-Sayed and Kh. W. Elkadeky, “Caratheodory theorem for a nonlocal problem of the differential equation ,” Alexandria Journal of Mathematics, vol. 1, no. 2, pp. 8–14, 2010.
- Y. Feng and S. Liu, “Existence, multiplicity and uniqueness results for a second order m-point boundary value problem,” Bulletin of the Korean Mathematical Society, vol. 41, no. 3, pp. 483–492, 2004.
- K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990.
- C. P. Gupta, “Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation,” Journal of Mathematical Analysis and Applications, vol. 168, no. 2, pp. 540–551, 1992.
- Y. Guo, Y. Ji, and J. Zhang, “Three positive solutions for a nonlinear nth-order m-point boundary value problem,” Nonlinear Analysis: Theory, Methods and Applications, vol. 68, no. 11, pp. 3485–3492, 2008.
- G. Infante and J. R. L. Webb, “Positive solutions of some nonlocal boundary value problems,” Abstract and Applied Analysis, vol. 2003, no. 18, pp. 1047–1060, 2003.
- A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis, Prentice-Hall, Englewood Cliffs, NJ, USA, 1970.
- 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.
- R. Liang, J. Peng, and J. Shen, “Positive solutions to a generalized second order three-point boundary value problem,” Applied Mathematics and Computation, vol. 196, no. 2, pp. 931–940, 2008.
- B. Liu, “Positive solutions of a nonlinear three-point boundary value problem,” Computers & Mathematics with Applications. An International Journal, vol. 44, no. 1-2, pp. 201–211, 2002.
- X. Liu, J. Qiu, and Y. Guo, “Three positive solutions for second-order m-point boundary value problems,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 733–742, 2004.
- R. Ma, “Positive solutions of a nonlinear three-point boundary-value problem,” Electronic Journal of Differential Equations, vol. 34, pp. 1–8, 1999.
- R. Ma, “Multiplicity of positive solutions for second-order three-point boundary value problems,” Computers & Mathematics with Applications, vol. 40, no. 2-3, pp. 193–204, 2000.
- R. Ma, “Positive solutions for second-order three-point boundary value problems,” Applied Mathematics Letters, vol. 14, no. 1, pp. 1–5, 2001.
- R. Ma and N. Castaneda, “Existence of solutions of nonlinear m-point boundary-value problems,” Journal of Mathematical Analysis and Applications, vol. 256, no. 2, pp. 556–567, 2001.
- S. K. Ntouyas, “Nonlocal initial and boundary value problems: a survey,” in Handbook of Differential Equations: Ordinary Differential Equations. Vol. II, A. Canada, P. Drabek, and A. Fonda, Eds., pp. 461–557, Elsevier, Amsterdam, The Netherlands, 2005.
- Y. Sun and X. Zhang, “Existence of symmetric positive solutions for an m-point boundary value problem,” Boundary Value Problems, vol. 2007, Article ID 79090, 14 pages, 2007.