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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 181052, 6 pages
Infinitely Many Solutions for a Class of Fractional Boundary Value Problems with Nonsmooth Potential
Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China
Received 4 June 2013; Accepted 8 August 2013
Academic Editor: Salvatore A. Marano
Copyright © 2013 Kaimin Teng. 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.
- F. H. Clarke, Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, New York, Ny, USA, 1983.
- S. Aizicovici, N. S. Papageorgiou, and V. Staicu, “Periodic solutions for second order differential inclusions with the scalar -Laplacian,” Journal of Mathematical Analysis and Applications, vol. 322, no. 2, pp. 913–929, 2006.
- L. Gasiński and N. S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, vol. 8 of Series in Mathematical Analysis and Applications, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2005.
- R. P. Agarwal, M. Belmekki, and M. Benchohra, “A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative,” Advances in Difference Equations, vol. 2009, Article ID 981728, 47 pages, 2009.
- B. Ahmad and V. Otero-Espinar, “Existence of solutions for fractional differential inclusions with antiperiodic boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 625347, 11 pages, 2009.
- M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, “Existence results for fractional functional differential inclusions with infinite delay and applications to control theory,” Fractional Calculus & Applied Analysis, vol. 11, no. 1, pp. 35–56, 2008.
- V. Lakshmikantham and A. S. Vatsala, “Basic theory of fractional differential equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 8, pp. 2677–2682, 2008.
- F. Jiao and Y. Zhou, “Existence results for fractional boundary value problem via critical point theory,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 22, no. 4, Article ID 1250086, 17 pages, 2012.
- G. Bonanno and G. M. Bisci, “Infinitely many solutions for a boundary value problem with discontinuous nonlinearities,” Boundary Value Problems, vol. 2009, Article ID 670675, 20 pages, 2009.
- S. A. Marano and D. Motreanu, “Infinitely many critical points of non-differentiable functions and applications to a Neumann-type problem involving the -Laplacian,” Journal of Differential Equations, vol. 182, no. 1, pp. 108–120, 2002.
- B. Ricceri, “A general variational principle and some of its applications,” Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 401–410, 2000.
- G. Bonanno and G. Molica Bisci, “Infinitely many solutions for a Dirichlet problem involving the -Laplacian,” Proceedings of the Royal Society of Edinburgh A, vol. 140, no. 4, pp. 737–752, 2010.
- G. Bonanno, G. M. Bisci, and D. O'Regan, “Infinitely many weak solutions for a class of quasilinear elliptic systems,” Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 152–160, 2010.
- G. A. Afrouzi and A. Hadjian, “Infinitely many solutions for a class of Dirichlet quasilinear elliptic systems,” Journal of Mathematical Analysis and Applications, vol. 393, no. 1, pp. 265–272, 2012.
- G. Bonanno and P. Candito, “Infinitely many solutions for a class of discrete non-linear boundary value problems,” Applicable Analysis, vol. 88, no. 4, pp. 605–616, 2009.
- G. D'Aguì, “Infinitely many solutions for a double Sturm-Liouville problem,” Journal of Global Optimization, vol. 54, no. 3, pp. 619–625, 2012.
- G. D'Aguì and A. Sciammetta, “Infinitely many solutions to elliptic problems with variable exponent and nonhomogeneous Neumann conditions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 75, no. 14, pp. 5612–5619, 2012.