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An ODE approach to the equation\(\Delta u + Ku^{\frac{{n + 2}}{{n - 2}}} = 0\), inR n, inR n

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References

  • [AP] Atkinson, F.V., Peletier, L.A.: Emden-Fowler equations involving critical exponents. Nonlinear Anal., Theory Methods Appl.10, 755–776 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • [BC] Bahri, A., Coron, J.-M.: The Scalar-curvature problem on the standard three-dimensional sphere. J. Funct. Anal.95, 106–172 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • [BE1] Bianchi, G., Egnell, H.: Local existence and uniqueness of positive solutions of the equation Δu+(1+ɛφ)u (n+2)/(n−2)=0, inR n and a related equation. In: Peletier, B. (ed.) Reaction diffusion equations and their equilibrium states. Proceedings, Gregynog 1989 (to appear)

  • [BE2] Bianchi, G., Egnell, H.: Work in progress

  • [BN] Brezis, H., Nirenberg, L.: Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Commun. Pure Appl. Math.36, 437–477 (1983)

    MATH  MathSciNet  Google Scholar 

  • [BP] Brezis, H., Peletier, L.A.: Asymptotics for elliptic equations involving critical growth. In: Colombini, F., Marino, A., Modica, L., Spagnolo, S. (eds) Partial Differential Equations and the Calculus of Variations, pp. 149–192. Boston Basel Stuttgart: Birkhäuser 1989

    Google Scholar 

  • [CS] Cheng, K.S., Smoller, J.: Conformal metrics with prescribed Gaussian curvature onS 2. Trans. Am. Math. Soc.

  • [CY] Chang, A., Yang, P.: Work in progress

  • [DN] Ding, W.-Y., Ni, W.-M.: On the elliptic equation Δu+Ku (n+2)/(n−2)=0 and related topics. Duke Math. J.52, 485–506 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  • [EG] Egnell, H.: Semilinear elliptic equations involving critical Sobolev exponents. Arch. Ration. Mech. Anal.104, 27–56 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • [ES] Escobar, J., Schoen, R.: Conformal metrics with prescribed scalar curvature. Invent. Math.86, 243–254 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • [KW] Kazdan, J., Warner, F.: Existence and conformal deformations of metrics with prescribed gaussian and scalar curvature. Ann. Math.101, 317–331 (1975)

    Article  MathSciNet  Google Scholar 

  • [LI] Lions, P.L.: The Concentration-compactness principle in the calculus of variation. The limit case. Rev. Mat. Iberoam.1(1), 145–201 (1985);1(2), 45–121 (1985)

    MATH  Google Scholar 

  • [LN] Li, Y., Ni, W.-M.: On the conformal scalar curvature equation inR n. Duke Math. J.57, 895–924 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • [NI1] Ni, W.-M.: On the elliptic equation Δu+K(x)u (n+2)/(n−2)=0, its generalizations, and applications in geometry. Indiana Univ. Math. J.31, 493–529 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  • [NI2] Ni, W.-M.: Some aspects of semilinear elliptic equations onR n In: Ni, W.-M. (ed.) Nonlinear diffusion equations and their equilibrium states, II, pp. 171–205. Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  • [PS] Pucci, P., Serrin, J.: A general variational identity. Indiana Univ. Math. J.35, 681–703 (1986)

    Article  MATH  MathSciNet  Google Scholar 

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Supported by a CNR fellowship

Supported in part by NSF Grant DMS-8914778

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Bianchi, G., Egnell, H. An ODE approach to the equation\(\Delta u + Ku^{\frac{{n + 2}}{{n - 2}}} = 0\), inR n, inR n . Math Z 210, 137–166 (1992). https://doi.org/10.1007/BF02571788

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