Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Variational methods for non-local operators of elliptic type
Pages: 2105 - 2137, Issue 5, May 2013

doi:10.3934/dcds.2013.33.2105      Abstract        References        Full text (418.8K)           Related Articles

Raffaella Servadei - Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31 B, Arcavacata di Rende (Cosenza), 87036, Italy (email)
Enrico Valdinoci - Dipartimento di Matematica, Università di Milano, Via Cesare Saldini 50, 20133 Milano, Italy (email)

1 A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381.       
2 H. Brézis, "Analyse Fonctionelle. Théorie et Applications," Masson, Paris, 1983.       
3 X. Cabré and J. Tan, Positive solutions of nonlinear problems involving the square root of the Laplacian, Adv. Math., 224 (2010), 2052-2093.       
4 E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., 136 (2012), 521-573.       
5 P. Felmer, A. Quaas and J. Tan, Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A.
6 P. H. Rabinowitz, Some critical point theorems and applications to semilinear elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 5 (1978), 215-223.       
7 P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math., 65, American, Mathematical Society, Providence, RI (1986).       
8 R. Servadei, The Yamabe equation in a non-local setting, preprint, available at http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=12-40.
9 R. Servadei and E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators, Rev. Mat. Iberoam., 29 (2013).
10 R. Servadei and E. Valdinoci, Mountain Pass solutions for non-local elliptic operators, J. Math. Anal. Appl., 389 (2012), 887-898.       
11 R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian, Trans. Amer. Math. Soc.
12 M. Struwe, "Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems," Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Springer Verlag, Berlin-Heidelberg, 1990.       
13 J. Tan, The Brezis-Nirenberg type problem involving the square root of the Laplacian, Calc. Var. Partial Differential Equations, 36 (2011), 21-41.       
14 M. Willem, "Minimax Theorems," Progress in Nonlinear Differential Equations and their Applications, 24, Birkhäuser, Boston, 1996.       

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