Abstract and Applied Analysis

Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces

Abstract

Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces.

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 831730, 8 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171120

Digital Object Identifier
doi:10.1155/2011/831730

Mathematical Reviews number (MathSciNet)
MR2771242

Zentralblatt MATH identifier
1217.34035

Citation

Cai, Jingjing; Liu, Guilong. Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces. Abstr. Appl. Anal. 2011 (2011), Article ID 831730, 8 pages. doi:10.1155/2011/831730. https://projecteuclid.org/euclid.aaa/1313171120

References

• R. P. Agarwal, “On fourth order boundary value problems arising in beam analysis,” Differential and Integral Equations, vol. 2, no. 1, pp. 91–110, 1989.
• C. de Coster, C. Fabry, and F. Munyamarere, “Nonresonance conditions for fourth order nonlinear boundary value problems,” International Journal of Mathematics and Mathematical Sciences, vol. 17, no. 4, pp. 725–740, 1994.
• D. Jiang, H. Liu, and X. Xu, “Nonresonant singular fourth-order boundary value problems,” Applied Mathematics Letters, vol. 18, no. 1, pp. 69–75, 2005.
• X. Lin, D. Jiang, and X. Li, “Existence and uniqueness of solutions for singular fourth-order boundary value problems,” Journal of Computational and Applied Mathematics, vol. 196, no. 1, pp. 155–161, 2006.
• L. Liu, X. Zhang, and Y. Wu, “Positive solutions of fourth-order nonlinear singular Sturm-Liouville eigenvalue problems,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1212–1224, 2007.
• R. Ma and H. Wang, “On the existence of positive solutions of fourth-order ordinary differential equations,” Applicable Analysis, vol. 59, no. 1–4, pp. 225–231, 1995.
• Q. L. Yao, “Existence of positive solutions of BVP for ${u}^{(4)}(t)-\lambda h(t)f(u(t))=0$,” Chinese Annals of Mathematics A, vol. 20, pp. 575–578, 1999.
• D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, vol. 373 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.