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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 740760, 14 pages
Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations
1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, Sichuan, China
2School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, Shandong, China
Received 22 October 2012; Accepted 19 November 2012
Academic Editor: Dragoş-Pătru Covei
Copyright © 2012 Jing Wu and Xinguang Zhang. 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.
- H. M. Srivastava and S. Owa, Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, New York, NY, USA, John Wiley and Sons, Chichester, UK, 1989.
- L. Gaul, P. Klein, and S. Kemple, “Damping description involving fractional operators,” Mechanical Systems and Signal Processing, vol. 5, no. 2, pp. 81–88, 1991.
- W. G. Glockle and T. F. Nonnenmacher, “A fractional calculus approach to self-similar protein dynamics,” Biophysical Journal, vol. 68, no. 1, pp. 46–53, 1995.
- K. Diethelm, The Analysis of Fractional Differential Equations, Springer-Verlag, Berlin, Germany, 2010.
- R. Metzler, W. Schick, H. G. Kilian, and T. F. Nonnenmacher, “Relaxation in filled polymers: a fractional calculus approach,” The Journal of Chemical Physics, vol. 103, no. 16, pp. 7180–7186, 1995.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, “Theory and applications of fractional differential equations,” in North-Holland Mathematics Studies, vol. 204, Elsevier, Amsterdam, The Netherlands, 2006.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999.
- X. Zhang, L. Liu, and Y. Wu, “Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 1420–1433, 2012.
- B. Ahmad, A. Alsaedi, and B. S. Alghamdi, “Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions,” Nonlinear Analysis: Real World Applications, vol. 9, no. 4, pp. 1727–1740, 2008.
- X. Zhang and Y. Han, “Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations,” Applied Mathematics Letters, vol. 25, no. 3, pp. 555–560, 2012.
- X. Zhang, L. Liu, and Y. Wu, “The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives,” Applied Mathematics and Computation, vol. 218, no. 17, pp. 8526–8536, 2012.
- X. Zhang, L. Liu, B. Wiwatanapataphee, and Y. Wu, “Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives,” Abstract and Applied Analysis, vol. 2012, Article ID 512127, 16 pages, 2012.
- X. Zhang, L. Liu, and Y. Wu, “Multiple positive solutions of a singular fractional differential equation with negatively perturbed term,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 1263–1274, 2012.
- H. A. H. Salem, “On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies,” Journal of Computational and Applied Mathematics, vol. 224, no. 2, pp. 565–572, 2009.
- C. S. Goodrich, “Existence of a positive solution to a class of fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1050–1055, 2010.
- M. Rehman and R. A. Khan, “Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1038–1044, 2010.
- B. Ahmad and J. J. Nieto, “Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions,” Boundary Value Problems, vol. 2011, 2011.
- C. S. Goodrich, “Existence of a positive solution to systems of differential equations of fractional order,” Computers and Mathematics with Applications, vol. 62, no. 3, pp. 1251–1268, 2011.
- C. S. Goodrich, “Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions,” Computers and Mathematics with Applications, vol. 61, no. 2, pp. 191–202, 2011.
- C. S. Goodrich, “Positive solutions to boundary value problems with nonlinear boundary conditions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 75, no. 1, pp. 417–432, 2012.
- M. Jia, X. Zhang, and X. Gu, “Nontrivial solutions for a higher fractional differential equation with fractional multi-point boundary conditions,” Boundary Value Problems, vol. 2012, 70 pages, 2012.
- M. Jia, X. Liu, and X. Gu, “Uniqueness and asymptotic behavior of positive solutions for a fractional-order integral boundary value problem,” Abstract and Applied Analysis, vol. 2012, Article ID 294694, 21 pages, 2012.
- P.-L. Lions, “On the existence of positive solutions of semilinear elliptic equations,” SIAM Review, vol. 24, no. 4, pp. 441–467, 1982.
- R. Aris, Introduction to the Analysis of Chemical Reactors, Prentice-Hall, Englewood Cliffs, NJ, USA, 1965.
- A. Castro, C. Maya, and R. Shivaji, “Nonlinear eigenvalue problems with semipositone,” Electronic Journal of Differential Equations, vol. 5, pp. 33–49, 2000.
- V. Anuradha, D. D. Hai, and R. Shivaji, “Existence results for superlinear semipositone BVP'S,” Proceedings of the American Mathematical Society, vol. 124, no. 3, pp. 757–763, 1996.
- D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cone, Academic Press, New York, NY, USA, 1988.