- 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 951251, 12 pages
Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Received 20 December 2011; Accepted 22 February 2012
Academic Editor: Yuriy Rogovchenko
Copyright © 2012 Chenghua Gao. 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.
- D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, Oxford Applied Mathematics and Computing Science Series, Clarendon Press, Oxford, UK, 1977.
- A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, Pure and Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1979.
- B. J. Lazan, Damping of Meterials in Structural Mechanics, Pergamon Press, Elmsford, NY, USA, 1968.
- N. Minorsky, Nonlinear Oscillations, Van Nostrand, Princeton, NJ, USA, 1962.
- E. M. Landesman and A. C. Lazer, “Nonlinear perturbations of linear elliptic boundary value problems at resonance,” Journal of Mathematics and Mechanics, vol. 19, pp. 609–623, 1969/1970.
- R. Iannacci and M. N. Nkashama, “Unbounded perturbations of forced second order ordinary differential equations at resonance,” Journal of Differential Equations, vol. 69, no. 3, pp. 289–309, 1987.
- R. Kannan, R. K. Nagle, and K. L. Pothoven, “Remarks on the existence of solutions of ; ,” Nonlinear Analysis: Theory, Methods & Applications, vol. 22, no. 6, pp. 793–796, 1994.
- A. Cañada and P. Drábek, “On semilinear problems with nonlinearities depending only on derivatives,” SIAM Journal on Mathematical Analysis, vol. 27, no. 2, pp. 543–557, 1996.
- P. Habets and L. Sanchez, “A two-point problem with nonlinearity depending only on the derivative,” SIAM Journal on Mathematical Analysis, vol. 28, no. 5, pp. 1205–1211, 1997.
- P. Drábek, P. Girg, and F. Roca, “Remarks on the range properties of certain semilinear problems of Landesman-Lazer type,” Journal of Mathematical Analysis and Applications, vol. 257, no. 1, pp. 131–140, 2001.
- N. Del Toro and F. Roca, “Existence and multiplicity of solutions for certain Dirichlet problems with nonlinearity depending on the derivative,” Nonlinear Analysis: Theory, Methods & Applications, vol. 55, no. 7-8, pp. 827–843, 2003.
- J. Rodriguez, “Nonlinear discrete Sturm-Liouville problems,” Journal of Mathematical Analysis and Applications, vol. 308, no. 1, pp. 380–391, 2005.
- R. Ma, “Nonlinear discrete Sturm-Liouville problems at resonance,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 11, pp. 3050–3057, 2007.
- R. Ma and H. Ma, “Unbounded perturbations of nonlinear discrete periodic problem at resonance,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 7, pp. 2602–2613, 2009.
- R. Ma and H. Ma, “Existence of sign-changing periodic solutions of second order difference equations,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 463–470, 2008.
- P. J. Y. Wong and R. P. Agarwal, “Fixed-sign solutions of a system of higher order difference equations,” Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 167–181, 2000.
- R. P. Agarwal and D. O'Regan, “Nonpositone discrete boundary value problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 39, no. 2, pp. 207–215, 2000.
- D. Bai and Y. Xu, “Nontrivial solutions of boundary value problems of second-order difference equations,” Journal of Mathematical Analysis and Applications, vol. 326, no. 1, pp. 297–302, 2007.
- J. Henderson, “Positive solutions for nonlinear difference equations,” Nonlinear Studies, vol. 4, no. 1, pp. 29–36, 1997.
- J. Henderson and H. B. Thompson, “Existence of multiple solutions for second-order discrete boundary value problems,” Computers & Mathematics with Applications, vol. 43, no. 10-11, pp. 1239–1248, 2002.
- R. Ma and Y. N. Raffoul, “Positive solutions of three-point nonlinear discrete second order boundary value problem,” Journal of Difference Equations and Applications, vol. 10, no. 2, pp. 129–138, 2004.
- J. Mawhin, “Topological degree and boundary value problems for nonlinear differential equations,” in Topological Methods for Ordinary Differential Equations, P. M. Fitzpatric, M. Matelli, J. Mawhin, and R. Nussbaum, Eds., vol. 1537 of Lecture Notes in Math., pp. 74–142, Springer, Berlin, Germany, 1993.