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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 809769, 7 pages
Three Weak Solutions for Nonlocal Fractional Laplacian Equations
Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu 223300, China
Received 16 September 2013; Revised 19 November 2013; Accepted 27 November 2013; Published 16 January 2014
Academic Editor: Salvatore A. Marano
Copyright © 2014 Dandan Yang and Chuanzhi Bai. 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.
- L. A. Caffarelli, S. Salsa, and L. Silvestre, “Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian,” Inventiones Mathematicae, vol. 171, no. 2, pp. 425–461, 2008.
- L. Silvestre, “Regularity of the obstacle problem for a fractional power of the Laplace operator,” Communications on Pure and Applied Mathematics, vol. 60, no. 1, pp. 67–112, 2007.
- X. Cabré and J. Tan, “Positive solutions of nonlinear problems involving the square root of the Laplacian,” Advances in Mathematics, vol. 224, no. 5, pp. 2052–2093, 2010.
- X. Cabré and Y. Sire, “Nonlinear equations for fractional Laplacians I: regularity, maximum principles, and Hamiltonian estimates,” Annales de l'Institut Henri Poincare C, 2013.
- E. Di Nezza, G. Palatucci, and E. Valdinoci, “Hitchhiker's guide to the fractional Sobolev spaces,” Bulletin des Sciences Mathématiques, vol. 136, no. 5, pp. 521–573, 2012.
- R. Servadei and E. Valdinoci, “Mountain pass solutions for non-local elliptic operators,” Journal of Mathematical Analysis and Applications, vol. 389, no. 2, pp. 887–898, 2012.
- R. Servadei and E. Valdinoci, “Variational methods for non-local operators of elliptic type,” Discrete and Continuous Dynamical Systems A, vol. 33, no. 5, pp. 2105–2137, 2013.
- R. Servadei and E. Valdinoci, “Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators,” Revista Matemática Iberoamericana, vol. 29, no. 3, pp. 1091–1126, 2013.
- M. M. Fall and T. Weth, “Nonexistence results for a class of fractional elliptic boundary value problems,” Journal of Functional Analysis, vol. 263, no. 8, pp. 2205–2227, 2012.
- F. Ferrari and I. E. Verbitsky, “Radial fractional Laplace operators and Hessian inequalities,” Journal of Differential Equations, vol. 253, no. 1, pp. 244–272, 2012.
- R. Servadei and E. Valdinoci, “The Brezis-Nirenberg result for the fractional Laplacian,” Transactions of the American Mathematical Society. In press.
- C. Bai, “Existence results for non-local operators of elliptic type,” Nonlinear Analysis A, vol. 83, pp. 82–90, 2013.
- S. Dipierro, G. Palatucci, and E. Valdinoci, “Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian,” Le Matematiche, vol. 68, no. 1, pp. 201–216, 2013.
- G. Bonanno and S. A. Marano, “On the structure of the critical set of non-differentiable functions with a weak compactness condition,” Applicable Analysis, vol. 89, no. 1, pp. 1–10, 2010.
- G. Bonanno and G. Molica Bisci, “Three weak solutions for elliptic Dirichlet problems,” Journal of Mathematical Analysis and Applications, vol. 382, no. 1, pp. 1–8, 2011.
- G. Molica Bisci and R. Servadei, “A bifurcation result for non-local fractional equations,” Journal of Applied Analysis. In press.
- G. Bonanno and P. Candito, “Three solutions to a Neumann problem for elliptic equations involving the -Laplacian,” Archiv der Mathematik, vol. 80, no. 4, pp. 424–429, 2003.
- E. Zeidler, Nonlinear Functional Analysis and Its Applications, vol. 2, Springer, New York, NY, USA, 1985.