References
Bahri, A. & Coron, J. M., On a nonlinear elliptic equation involving the Sobolev exponent: the effect of the topology of the domain. Comm. Pure Appl. Math. 41 (1988), 253–294.
Benci, V. & Cerami, G., Positive solutions of some nonlinear elliptic problems in exterior domains. Arch. Rational Mech. Anal. 99 (1987), 283–300.
Benci, V. & Cerami, G., In preparation.
Brezis, H. & Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 36 (1983), 437–477.
Brezis, H. & Oswald, L., Remarks on sublinear elliptic equations, Nonlinear Analysis T.M.A. 10 (1986), 55–64.
Coron, J. M., Topologie et cas limite des injections de Sobolev. C. R. Ac. Se. Paris 299, Séries I (1984), 209–212.
Dancer, E. N., The effect of domain shape on the number of positive solutions of certain nonlinear equations. J. Diff. Equations 74 (1988), 120–156.
Dancer, E. N., A note on an equation with critical exponent. Bull. London Math. Soc. 20 (1988), 600–602.
Ding, W. Y., Positive solutions of Δu + uN+2 N−2=0 on contractible domains, preprint.
Gidas, B., Ni, W. M. & Nirenberg, L., Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68 (1979), 209–243.
Gidas, B., Ni, W. M. & Nirenberg, L., Symmetry of positive solutions of nonlinear elliptic equations in RN. Mathematical Analysis and Applications: Part A. Advances in Mathematics Supplementary Studies. Vol. 7 A, 369–402.
Krasnoselskii, M., Positive solutions of operator equations, Noordhoff, Groningen (1964).
Lions, P. L., The concentration-compactness principle in the calculus of variations. The limit case I–II. Revista Mat. Iberoamericana 1.1 (1985), 145–200 / 1.2 (1985), 45–121.
Ni, W. M. & Nussbaum, R. D., Uniqueness and nonuniqueness for positive radial solutions of Δu + f(u,r) = 0, Comm. Pure Appl. Math. 38 (1985).
Passaseo, D., Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains. Manuscripta Math. 65 (1989), 147–166.
Strauss, W. A., Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977), 149–162.
Struwe, M., A global compactness result for elliptic boundary value problems involving limiting nonlinearities. Math. Z. 187 (1984), 511–517.
Rey, O., About a nonlinear equation involving the critical Sobolev exponent. Preprint.
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Communicated by H. Brezis
Dedicated to G. Prodi for his 65 th birthday
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Benci, V., Cerami, G. The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems. Arch. Rational Mech. Anal. 114, 79–93 (1991). https://doi.org/10.1007/BF00375686
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DOI: https://doi.org/10.1007/BF00375686