Multiple solutions of a nonlinear elliptic equation involving Neumann conditions and a critical Sobolev exponent
Rendiconti del Seminario Matematico della Università di Padova, Tome 110 (2003), pp. 1-24. 
@article{RSMUP_2003__110__1_0,
     author = {Chabrowski, J. and Yang, Jianfu},
     title = {Multiple solutions of a nonlinear elliptic equation involving {Neumann} conditions and a critical {Sobolev} exponent},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {1--24},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {110},
     year = {2003},
     mrnumber = {2032999},
     zbl = {1115.35042},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2003__110__1_0/}
}
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Chabrowski, J.; Yang, Jianfu. Multiple solutions of a nonlinear elliptic equation involving Neumann conditions and a critical Sobolev exponent. Rendiconti del Seminario Matematico della Università di Padova, Tome 110 (2003), pp. 1-24. http://archive.numdam.org/item/RSMUP_2003__110__1_0/

[1] Adimurthi - G. Mancini, The Neumann problem for elliptic equations with critical nonlinearity, A tribute in honor of G. Prodi, Scuola Norm. Sup. Pisa (1991), pp. 9-25. | MR | Zbl

[2] Adimurthi - G. Mancini, Effect of geometry and topology of the boundary in critical Neumann problem, J. Reine Angew. Math., 456 (1994), pp. 1-18. | MR | Zbl

[3] Adimurthi - G. Mancini - S. L. Yadava, The role of the mean curvature in a semilinear Neumann problem involving critical exponent, Comm. in P.D.E., 20, No. 3 and 4 (1995), pp. 591-631. | MR | Zbl

[4] Adimurthi - F. Pacella - S. L. Yadava, Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity, J. Funct. Anal., 113 (1993), pp. 318-350. | MR | Zbl

[5] Adimurthi - F. Pacella - S. L. Yadava, Characterization of concentration points and LQ -estimates for solutions of a semilinear Neumann problem involving the critical Sobolev exponent, Diff. Int. Eq., 8 (1995), pp. 31-68. | Zbl

[6] Adimurthi - S. L. Yadava, Critical Sobolev exponent problem in RN (NF4) with Neumann boundary condition, Proc. Indian Acad. Sci., 100 (1990), pp. 275-284. | MR | Zbl

[7] H. Brézis - L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Commun. Pure Appl. Math., 36 (1983), pp. 437-477. | MR | Zbl

[8] J. Chabrowski, On the nonlinear Neumann problem with indefinite weight and Sobolev critical nonlinearity, Bull. Pol. Acad. Sc., 50 (3) (2002), pp. 323-333. | MR

[9] J. Chabrowski, Mean curvature and least energy solutions for the critical Neumann problem with weight, B.U.M.I. B, 5 (8) (2002), pp. 715-733. | MR | Zbl

[10] J. Chabrowski - M. Willem, Least energy solutions of a critical Neumann problem with weight, Calc. Var., 15 (2002), pp. 121-131. | MR

[11] J. F. Escobar, Positive solutions for some nonlinear elliptic equations with critical Sobolev exponents, Commun. Pure Appl. Math., 40 (1987), pp. 623-657. | MR | Zbl

[12] G. Djairo De Figueiredo - Jianfu Yang, Critical superlinear AmbrosettiProdi problems, TMNA, 14 (1999), pp. 50-80. | Zbl

[13] D. Gilbarg - N. S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin (1983) (second edition). | MR | Zbl

[14] P. L. Lions, The concentration-compactness principle in the calculus of variations, The limit case, Revista Math. Iberoamericana, 1, No. 1 and No. 2 (1985), pp. 145-201 and pp. 45-120. | MR

[15] W. M. Ni - X. B. Pan - L. Takagi, Singular behavior of least energy solutions of a semilinear Neumann problem involving critical Sobolev exponent, Duke Math. J., 67 (1992), pp. 1-20. | MR | Zbl

[16] W. M. Ni - L. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math., 44 (1991), pp. 819-851. | MR | Zbl

[17] X. J. Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Diff. Eq., 93 (1991), 283-310. | MR | Zbl

[18] Z. Q. Wang, Remarks on a nonlinear Neumann problem with critical exponent, Houston J. Math., 20, No. 4 (1994), pp. 671-694. | MR | Zbl

[19] Z. Q. Wang, The effect of the domain geometry on number of positive solutions of Neumann problems with critical exponents, Diff. Int. Eq., 8, No. 6 (1995), pp. 1533-1554. | MR | Zbl

[20] M. Willem, Min-max Theorems, Boston 1996, Birkhäuser.