- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- 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 2011 (2011), Article ID 543035, 13 pages
Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems
Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
Received 31 December 2010; Accepted 23 March 2011
Academic Editor: Yuri V. Rogovchenko
Copyright © 2011 J. Caballero 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.
- A. Cabada, J. A. Cid, and L. Sánchez, “Positivity and lower and upper solutions for fourth order boundary value problems,” Nonlinear Analysis, vol. 67, no. 5, pp. 1599–1612, 2007.
- J. Ehme, P. W. Eloe, and J. Henderson, “Upper and lower solution methods for fully nonlinear boundary value problems,” Journal of Differential Equations, vol. 180, no. 1, pp. 51–64, 2002.
- D. Franco, D. O'Regan, and J. Perán, “Fourth-order problems with nonlinear boundary conditions,” Journal of Computational and Applied Mathematics, vol. 174, no. 2, pp. 315–327, 2005.
- F. Minhós, T. Gyulov, and A. I. Santos, “Existence and location result for a fourth order boundary value problem,” Discrete and Continuous Dynamical System Suplement, vol. 2005, pp. 662–671, 2005.
- Z. Bai, “The method of lower and upper solutions for a bending of an elastic beam equation,” Journal of Mathematical Analysis and Applications, vol. 248, no. 1, pp. 195–202, 2000.
- Y. Guo and Y. Gao, “The method of upper and lower solutions for a Lidstone boundary value problem,” Czechoslovak Mathematical Journal, vol. 55, no. 3, pp. 639–652, 2005.
- P. Habets and L. Sánchez, “A monotone method for fourth order boundary value problems involving a factorizable linear operator,” Portugaliae Mathematica, vol. 64, no. 3, pp. 255–279, 2007.
- J. Caballero, J. Harjani, and K. Sadarangani, “Existence and uniqueness of positive and non-decreasing solutions for a class of singular fractional boundary value problem,” Boundary Value Problems, vol. 2009, Article ID 421310, 2009.
- Z. Bai and H. Wang, “On positive solutions of some nonlinear fourth order beam equations,” Journal of Mathematical Analysis and Applications, vol. 270, no. 2, pp. 357–368, 2002.
- X. L. Liu and W. T. Li, “Existence and multiplicity of solutions for fourth-order boundary value problems with parameters,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 362–375, 2007.
- J. R. L. Webb, G. Infante, and D. Franco, “Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions,” Proceedings of the Royal Society of Edinburgh, vol. 138, no. 2, pp. 427–446, 2008.
- C. P. Gupta, “Existence and uniqueness theorems for some fourth order fully quasilinear boundary value problems,” Applicable Analysis, vol. 36, no. 3-4, pp. 157–169, 1990.
- G. E. Hernández and R. Manasevich, “Existence and multiplicity of solutions of a fourth order equation,” Applicable Analysis, vol. 54, no. 3-4, pp. 237–250, 1994.
- P. Korman, “Uniqueness and exact multiplicity of solutions for a class of fourth-order semilinear problems,” Proceedings of the Royal Society of Edinburgh, vol. 134, no. 1, pp. 179–190, 2004.
- R. Ma, “Existence of positive solutions of a fourth-order boundary value problem,” Applied Mathematics and Computation, vol. 168, no. 2, pp. 1219–1231, 2005.
- B. P. Rynne, “Infinitely many solutions of superlinear fourth order boundary value problems,” Topological Methods in Nonlinear Analysis, vol. 19, no. 2, pp. 303–312, 2002.
- A. Amini-Harandi and H. Emami, “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations,” Nonlinear Analysis, vol. 72, no. 5, pp. 2238–2242, 2010.
- J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005.
- M. Pei and S. K. Chang, “Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem,” Mathematical and Computer Modelling, vol. 51, no. 9-10, pp. 1260–1267, 2010.