Abstract
We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem:
Research Article | Open Access
Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation
Academic Editor: Ferhan Merdivenci Atici
Received16 May 2007
Revised24 Jul 2007
Accepted26 Sept 2007
Published31 Oct 2007
References
D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988.
View at: Google Scholar | Zentralblatt MATH | MathSciNetH. Wang, “On the existence of positive solutions for semilinear elliptic equations in the annulus,” Journal of Differential Equations, vol. 109, no. 1, pp. 1–7, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetZ. Bai and H. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetI. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Zhang, “Existence of solution for a boundary value problem of fractional order,” Acta Mathematica Scientia, vol. 26, no. 2, pp. 220–228, 2006.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Zhang, “Positive solutions for boundary-value problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations, vol. 2006, no. 36, pp. 1–12, 2006.
View at: Google Scholar | MathSciNetH. Amann, “Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces,” SIAM Review, vol. 18, no. 4, pp. 620–709, 1976.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. A. Krasnosel'skiĭ, Positive Solutions of Operator Equations, P. Noordhoff, Groningen, The Netherlands, 1964.
View at: Google Scholar | Zentralblatt MATH | MathSciNetH.-R. Sun and W.-K. Wen, “On the number of positive solutions for a nonlinear third order boundary value problem,” International Journal of Difference Equations, vol. 1, no. 1, pp. 165–176, 2006.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2007 Moustafa El-Shahed. 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.