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Volumn 2, Issue 3, 2013, Pages 235-270

The Yamabe equation in a non-local setting

Author keywords

Best fractional critical Sobolev constant; Critical nonlinearities; Fractional Laplacian; Integrodifferential operators; Linking Theorem; Mountain Pass Theorem; Palais Smale condition; Variational techniques

Indexed keywords


EID: 84885802074     PISSN: 21919496     EISSN: 2191950X     Source Type: Journal    
DOI: 10.1515/anona-2013-0008     Document Type: Article
Times cited : (102)

References (22)
  • 2
    • 47949110211 scopus 로고    scopus 로고
    • Nonlinear analysis and semilinear elliptic problems
    • Cambridge University Press, Cambridge
    • A. Ambrosetti and A. Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems, Cambridge Stud. Adv. Math. 104, Cambridge University Press, Cambridge, 2007.
    • (2007) Cambridge Stud. Adv. Math. , vol.104
    • Ambrosetti, A.1    Malchiodi, A.2
  • 3
    • 34548350707 scopus 로고
    • Dual variational methods in critical point theory and applications
    • A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.
    • (1973) J. Funct. Anal. , vol.14 , pp. 349-381
    • Ambrosetti, A.1    Rabinowitz, P.2
  • 6
    • 84980148463 scopus 로고
    • Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz
    • H. Brezis, J. M. Coron and L. Nirenberg, Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, Comm. Pure Appl. Math. 33 (1980), no. 5, 667-684.
    • (1980) Comm. Pure Appl. Math. , vol.33 , Issue.5 , pp. 667-684
    • Brezis, H.1    Coron, J.M.2    Nirenberg, L.3
  • 7
    • 84941275804 scopus 로고
    • A relation between pointwise convergence of functions and convergence of functionals
    • H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983), no. 3, 486-490.
    • (1983) Proc. Amer. Math. Soc. , vol.88 , Issue.3 , pp. 486-490
    • Brezis, H.1    Lieb, E.2
  • 8
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
    • H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), no. 4, 437-477.
    • (1983) Comm. Pure Appl. Math. , vol.36 , Issue.4 , pp. 437-477
    • Brezis, H.1    Nirenberg, L.2
  • 9
    • 85012023027 scopus 로고
    • An existence result for nonlinear elliptic problems involving critical sobolev exponent
    • A. Capozzi, D. Fortunato and G. Palmieri, An existence result for nonlinear elliptic problems involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), no. 6, 463-470.
    • (1985) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.2 , Issue.6 , pp. 463-470
    • Capozzi, A.1    Fortunato, D.2    Palmieri, G.3
  • 10
    • 3142718182 scopus 로고    scopus 로고
    • Best constants for sobolev inequalities for higher order fractional derivatives
    • A. Cotsiolis and N. Tavoularis, Best constants for Sobolev inequalities for higher order fractional derivatives, J. Math. Anal. Appl. 295 (2004), 225-236.
    • (2004) J. Math. Anal. Appl. , vol.295 , pp. 225-236
    • Cotsiolis, A.1    Tavoularis, N.2
  • 11
    • 84863469913 scopus 로고    scopus 로고
    • Hitchhiker's guide to the fractional sobolev spaces
    • E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math. 136 (2012), no. 5, 521-573.
    • (2012) Bull. Sci. Math. , vol.136 , Issue.5 , pp. 521-573
    • Di Nezza, E.1    Palatucci, G.2    Valdinoci, E.3
  • 12
    • 0008025841 scopus 로고    scopus 로고
    • Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations
    • F. Gazzola and B. Ruf, Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations, Adv. Differential Equations 2 (1997), no. 4, 555-572.
    • (1997) Adv. Differential Equations , vol.2 , Issue.4 , pp. 555-572
    • Gazzola, F.1    Ruf, B.2
  • 13
    • 0343987648 scopus 로고
    • Some critical point theorems and applications to semilinear elliptic partial differential equations
    • PH. Rabinowitz, Some critical point theorems and applications to semilinear elliptic partial differential equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 5 (1978), 215-223.
    • (1978) Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) , vol.5 , pp. 215-223
    • Rabinowitz, P.H.1
  • 14
    • 0001901435 scopus 로고
    • Minimax methods in critical point theory with applications to differential equations
    • American Mathematical Society, Providence
    • PH. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math. 65, American Mathematical Society, Providence, 1986.
    • (1986) CBMS Reg. Conf. Ser. Math. , vol.65
    • Rabinowitz, P.H.1
  • 15
    • 84856270145 scopus 로고    scopus 로고
    • Mountain pass solutions for non-local elliptic operators
    • R. Servadei and E. Valdinoci, Mountain pass solutions for non-local elliptic operators, J. Math. Anal. Appl. 389 (2012), 887-898.
    • (2012) J. Math. Anal. Appl. , vol.389 , pp. 887-898
    • Servadei, R.1    Valdinoci, E.2
  • 16
    • 84878285487 scopus 로고    scopus 로고
    • A brezis-nirenberg result for non-local critical equations in low dimension
    • R. Servadei and E. Valdinoci, A Brezis-Nirenberg result for non-local critical equations in low dimension, Commun. Pure Appl. Anal. 12 (2013), no. 6, 2445-2464.
    • (2013) Commun. Pure Appl. Anal. , vol.12 , Issue.6 , pp. 2445-2464
    • Servadei, R.1    Valdinoci, E.2
  • 17
    • 84872157074 scopus 로고    scopus 로고
    • Variational methods for non-local operators of elliptic type
    • R. Servadei and E. Valdinoci, Variational methods for non-local operators of elliptic type, Discrete Contin. Dyn. Syst. 33 (2013), no. 5, 2105-2137.
    • (2013) Discrete Contin. Dyn. Syst. , vol.33 , Issue.5 , pp. 2105-2137
    • Servadei, R.1    Valdinoci, E.2
  • 18
    • 84872149084 scopus 로고    scopus 로고
    • Lewy-stampacchia type estimates for variational inequalities driven by (non)local operators
    • to appear
    • R. Servadei and E. Valdinoci, Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators, Rev. Mat. Iberoam. 29 (2013), to appear.
    • (2013) Rev. Mat. Iberoam. , vol.29
    • Servadei, R.1    Valdinoci, E.2
  • 19
    • 84872144631 scopus 로고    scopus 로고
    • The brezis-nirenberg result for the fractional laplacian
    • to appear
    • R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian, Trans. Amer. Math. Soc., to appear.
    • Trans. Amer. Math. Soc.
    • Servadei, R.1    Valdinoci, E.2
  • 20
    • 84859630809 scopus 로고
    • Variational methods. Applications to nonlinear partial differential equations and hamiltonian systems
    • Springer-Verlag, Berlin
    • M. Struwe, Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Ergeb. Math. Grenzgeb. (3) 34, Springer-Verlag, Berlin, 1990.
    • (1990) Ergeb. Math. Grenzgeb. (3) , vol.34
    • Struwe, M.1
  • 21
    • 79960461967 scopus 로고    scopus 로고
    • The brezis-nirenberg type problem involving the square root of the laplacian
    • J. Tan, The Brezis-Nirenberg type problem involving the square root of the Laplacian, Calc. Var. Partial Differential Equations 36 (2011), no. 1-2, 21-41.
    • (2011) Calc. Var. Partial Differential Equations , vol.36 , Issue.1-2 , pp. 21-41
    • Tan, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.