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Variational methods for non-local operators of elliptic type
1. | Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci 31 B, Arcavacata di Rende (Cosenza), 87036 |
2. | Dipartimento di Matematica, Università di Milano, Via Cesare Saldini 50, 20133 Milano, Italy |
References:
[1] |
A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications,, J. Funct. Anal., 14 (1973), 349.
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[2] |
H. Brézis, "Analyse Fonctionelle. Théorie et Applications,", Masson, (1983).
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[3] |
X. Cabré and J. Tan, Positive solutions of nonlinear problems involving the square root of the Laplacian,, Adv. Math., 224 (2010), 2052.
doi: 10.1016/j.aim.2010.01.025. |
[4] |
E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces,, Bull. Sci. Math., 136 (2012), 521.
doi: 10.1016/j.bulsci.2011.12.004. |
[5] |
P. Felmer, A. Quaas and J. Tan, Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian,, Proc. Roy. Soc. Edinburgh Sect. A., (). Google Scholar |
[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.
|
[7] |
P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations,, CBMS Reg. Conf. Ser. Math., (1986).
|
[8] |
R. Servadei, The Yamabe equation in a non-local setting,, preprint, (): 12. Google Scholar |
[9] |
R. Servadei and E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators,, Rev. Mat. Iberoam., 29 (2013). Google Scholar |
[10] |
R. Servadei and E. Valdinoci, Mountain Pass solutions for non-local elliptic operators,, J. Math. Anal. Appl., 389 (2012), 887.
doi: 10.1016/j.jmaa.2011.12.032. |
[11] |
R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian,, Trans. Amer. Math. Soc., (). Google Scholar |
[12] |
M. Struwe, "Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems,", Ergebnisse der Mathematik und ihrer Grenzgebiete, 3 (1990).
|
[13] |
J. Tan, The Brezis-Nirenberg type problem involving the square root of the Laplacian,, Calc. Var. Partial Differential Equations, 36 (2011), 21.
doi: 10.1007/s00526-010-0378-3. |
[14] |
M. Willem, "Minimax Theorems,", Progress in Nonlinear Differential Equations and their Applications, 24 (1996).
doi: 10.1007/978-1-4612-4146-1. |
show all references
References:
[1] |
A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications,, J. Funct. Anal., 14 (1973), 349.
|
[2] |
H. Brézis, "Analyse Fonctionelle. Théorie et Applications,", Masson, (1983).
|
[3] |
X. Cabré and J. Tan, Positive solutions of nonlinear problems involving the square root of the Laplacian,, Adv. Math., 224 (2010), 2052.
doi: 10.1016/j.aim.2010.01.025. |
[4] |
E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces,, Bull. Sci. Math., 136 (2012), 521.
doi: 10.1016/j.bulsci.2011.12.004. |
[5] |
P. Felmer, A. Quaas and J. Tan, Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian,, Proc. Roy. Soc. Edinburgh Sect. A., (). Google Scholar |
[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.
|
[7] |
P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations,, CBMS Reg. Conf. Ser. Math., (1986).
|
[8] |
R. Servadei, The Yamabe equation in a non-local setting,, preprint, (): 12. Google Scholar |
[9] |
R. Servadei and E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators,, Rev. Mat. Iberoam., 29 (2013). Google Scholar |
[10] |
R. Servadei and E. Valdinoci, Mountain Pass solutions for non-local elliptic operators,, J. Math. Anal. Appl., 389 (2012), 887.
doi: 10.1016/j.jmaa.2011.12.032. |
[11] |
R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian,, Trans. Amer. Math. Soc., (). Google Scholar |
[12] |
M. Struwe, "Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems,", Ergebnisse der Mathematik und ihrer Grenzgebiete, 3 (1990).
|
[13] |
J. Tan, The Brezis-Nirenberg type problem involving the square root of the Laplacian,, Calc. Var. Partial Differential Equations, 36 (2011), 21.
doi: 10.1007/s00526-010-0378-3. |
[14] |
M. Willem, "Minimax Theorems,", Progress in Nonlinear Differential Equations and their Applications, 24 (1996).
doi: 10.1007/978-1-4612-4146-1. |
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