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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 324848, 9 pages
Existence Results for a Coupled System of Nonlinear Fourth-Order Differential Equations
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Received 10 November 2013; Accepted 3 December 2013
Academic Editor: Mohamed Boussairi Jleli
Copyright © 2013 Bessem Samet. 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, “A nonlinear boundary-value problem associated with the static equilibrium of an elastic beam supported by sliding clamps,” International Journal of Mathematics and Mathematical Sciences, vol. 12, no. 4, pp. 697–711, 1989.
- G. Bonanno and B. Di Bella, “A boundary value problem for fourth-order elastic beam equations,” Journal of Mathematical Analysis and Applications, vol. 343, no. 2, pp. 1166–1176, 2008.
- C. J. Chyan and J. Henderson, “Positive solutions of 2mth-order boundary value problems,” Applied Mathematics Letters, vol. 15, no. 6, pp. 767–774, 2002.
- J. R. Graef and B. Yang, “On a nonlinear boundary value problem for fourth order equations,” Journal of Applied Analysis, vol. 72, pp. 439–448, 1999.
- C. P. Gupta, “Existence and uniqueness theorems for the bending of an elastics beam equation,” Journal of Applied Analysis, vol. 26, no. 4, pp. 289–304, 1988.
- P. Kang and L. Liu, “Positive solutions of fourth order singular boundary value problems,” Journal of Systems Science and Mathematical Sciences, vol. 28, pp. 604–615, 2008 (Chinese).
- Y. Li, “On the existence of positive solutions for the bending elastic beam equations,” Applied Mathematics and Computation, vol. 189, no. 1, pp. 821–827, 2007.
- Q. Yao, “Existence of n solutions and/or positive solutions to a semipositone elastic beam equation,” Nonlinear Analysis: Theory, Methods and Applications, vol. 66, no. 1, pp. 138–150, 2007.
- R. P. Agarwal, “On fourth order boundary value problems arising in beam analysis,” Differential Integral Equations, vol. 2, pp. 91–110, 1989.
- 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.
- M. A. del Pino and R. F. Manasevich, “Existence for a fourth-order boundary value problem under a two parameter nonresonance condition,” Proceedings of the American Mathematical Society, vol. 112, pp. 81–86, 1991.
- D. R. Dunninger, “Multiplicity of positive solutions for a nonlinear fourth order equation,” Annales Polonici Mathematici, vol. 77, no. 2, pp. 161–168, 2001.
- D. O'Regan, “Solvability of some fourth (and higher) order singular boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 161, no. 1, pp. 78–116, 1991.
- P. Kang and Z. Wei, “Existence of positive solutions for systems of bending elastic beam equations,” Electronic Journal of Differential Equations, vol. 2012, pp. 1–9, 2012.
- A. I. Perov, “On the Cauchy problem for a system of ordinary differential equations,” Pviblizhen. Met. Reshen. Differ. Uvavn, vol. 2, pp. 115–134, 1964.
- D. A. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, vol. 224, Springer, Berlin, Germany, 2001.
- J. X. Sun, Nonlinear Functional Analysis and Its Application, Science Press, Beijing, China, 2008.
- R. P. Agarwal, Y. Zhou, and Y. He, “Existence of fractional neutral functional differential equations,” Computers and Mathematics with Applications, vol. 59, no. 3, pp. 1095–1100, 2010.