Duke Mathematical Journal

A class of solutions for the Neumann problem $-\Delta u + \lambda u = u^{(N+2)/(N-2)}$

Massimo Grossi
Source: Duke Math. J. Volume 79, Number 2 (1995), 309-334.
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Primary Subjects: 35J65
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077285155
Mathematical Reviews number (MathSciNet): MR1344764
Zentralblatt MATH identifier: 00815779
Digital Object Identifier: doi:10.1215/S0012-7094-95-07908-3

References

[AM1] Adimurthi and G. Mancini, The Neumann problem for elliptic equations with critical nonlinearity, Nonlinear Analysis, Quaderni, Scuola Norm. Sup., Pisa, 1991, pp. 9–25.
Mathematical Reviews (MathSciNet): MR94d:35043
Zentralblatt MATH: 0836.35048
[AM2] Adimurthi and G. Mancini, Effect of geometry and topology of the boundary in the critical Neumann problem, preprint.
[APY] Adimurthi, F. Pacella, and 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), no. 2, 318–350.
Mathematical Reviews (MathSciNet): MR94e:35030
Zentralblatt MATH: 0793.35033
Digital Object Identifier: doi:10.1006/jfan.1993.1053
[BC] A. Bahri and J. M. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent: The effect of the topology of the domain, Comm. Pure Appl. Math. 41 (1988), no. 3, 253–294.
Mathematical Reviews (MathSciNet): MR89c:35053
Zentralblatt MATH: 0649.35033
Digital Object Identifier: doi:10.1002/cpa.3160410302
[GP] M. Grossi and F. Pacella, Positive solutions of nonlinear elliptic equations with critical Sobolev exponent and mixed boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 116 (1990), no. 1-2, 23–43.
Mathematical Reviews (MathSciNet): MR91m:35027
Zentralblatt MATH: 0724.35041
[H] H. Hofer, Variational and topological methods in partially ordered Hilbert spaces, Math. Ann. 261 (1982), no. 4, 493–514.
Mathematical Reviews (MathSciNet): MR84g:58030
Zentralblatt MATH: 0488.47034
Digital Object Identifier: doi:10.1007/BF01457453
[L1]1 P. L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. I, Rev. Mat. Iberoamericana 1 (1985), no. 1, 145–201.
Mathematical Reviews (MathSciNet): MR87c:49007
Zentralblatt MATH: 0704.49005
[L1]2 P. L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. II, Rev. Mat. Iberoamericana 1 (1985), no. 2, 45–121.
Mathematical Reviews (MathSciNet): MR87j:49012
Zentralblatt MATH: 0704.49006
[L2] P. L. Lions, Applications de la méthode de concentration-compacité à l'existence de fonctions extrémales, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 15, 645–648.
Mathematical Reviews (MathSciNet): MR85b:49023
Zentralblatt MATH: 0522.49008
[Pa] D. Passaseo, Multiplicity of positive solutions for the equation $\Delta u+ \lambda u+ u^2^*-1 =0$ in noncontractible domains, to appear.
Mathematical Reviews (MathSciNet): MR1251943
Zentralblatt MATH: 0810.35029
[Po] S. Pohozaev, Eigenfunctions of the equations $\Delta u+\lambda f(u)=0$, Soviet Math. Dokl. 6 (1965), 1408–1411.
[R] O. Rey, The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990), no. 1, 1–52.
Mathematical Reviews (MathSciNet): MR91b:35012
Zentralblatt MATH: 0786.35059
Digital Object Identifier: doi:10.1016/0022-1236(90)90002-3
[S1] M. Struwe, Variational Methods, Springer-Verlag, Berlin, 1990.
Mathematical Reviews (MathSciNet): MR92b:49002
Zentralblatt MATH: 0746.49010
[S2] M. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z. 187 (1984), no. 4, 511–517.
Mathematical Reviews (MathSciNet): MR86k:35046
Zentralblatt MATH: 0545.35034
Digital Object Identifier: doi:10.1007/BF01174186
[W1] X. J. Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Differential Equations 93 (1991), no. 2, 283–310.
Mathematical Reviews (MathSciNet): MR92j:35072
Zentralblatt MATH: 0766.35017
Digital Object Identifier: doi:10.1016/0022-0396(91)90014-Z
[W2] Z. Q. Wang, The effect of the domain geometry on the number of positive solutions of Neumann problems with critical exponent, to appear.
Mathematical Reviews (MathSciNet): MR1329855

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