References
A. Bahri & J.-M. Coron, The Scalar-Curvature Problem on the Standard Three-dimensional Sphere. J. Funct. Anal. 95 (1991) 106–172.
G. Bianchi & H. Egnell, Local Existence and Uniqueness of Positive Solutions of the Equation \(\Delta u + (1 + \varepsilon \varphi )u^{\frac{{n + 2}}{{n - 2}}} = 0\), in R n and a Related Equation. In: N. G. Lloyd, W. M. Ni, L. A. Peletier & J. Serrin (eds.) Nonlinear Diffusion Equations and their Equilibrium States. Proceeedings, Gregynog 1989, pp. 111–128, Birkhäuser, 1992.
G. Bianchi & H. Egnell, An ODE Approach to the Equation \(\Delta u + Ku^{\frac{{n + 2}}{{n - 2}}} = 0\), in R n. Math. Z. 210 (1992) 137–166.
G. Bianchi & H. Egnell, A Note on the Sobolev Inequality. J. Funct. Anal. 100 (1991) 18–24.
A. Chang & P. Yang, A Perturbation Result in Prescribing Scalar Curvature on S n. Preprint.
W.-Y. Ding & W.-M. Ni, On the Elliptic Equation \(\Delta u + Ku^{\frac{{n + 2}}{{n - 2}}} = 0\) and Related Topics. Duke Math. J. 52 (1985) 485–506.
H. Egnell, Positive Solutions of Semilinear Elliptic Equations in Cones. Trans. Amer. Math. Soc. (to appear).
H. Egnell, Asymptotic Results for Finite Energy Solutions of Semilinear Elliptic Equations. J. Diff. Eqs. (to appear).
J. Escobar & R. Schoen, Conformal Metrics with Prescribed Scalar Curvature. Invent. Math. 86 (1986) 243–254.
J. Kazdan & F. Warner, Existence and Conformal Deformations of Metrics with Prescribed Gaussian and Scalar Curvature. Ann. of Math. 101 (1975) 317–331.
P. L. Lions, The Concentration-Compactness Principle in the Calculus of Variation. The limit case. Rev. Mat. Ibero. 1-1 (1985) 145–201; 1–2 (1985) 45–121.
C.-S. Lin & S.-S. Lin, Positive Radial Solutions for \(\Delta u + Ku^{\frac{{n + 2}}{{n - 2}}} = 0\) and related topics. Appl. Anal. 38 (1990) 121–159.
M. Struwe, A Global Compactness Result for Elliptic Boundary Problems Involving Limiting Nonlinearities. Math. Z. 187 (1984) 511–517.
Author information
Authors and Affiliations
Additional information
Communicated by J. Serrin
Rights and permissions
About this article
Cite this article
Bianchi, G., Egnell, H. A variational approach to the equation \(\Delta u + Ku^{\frac{{n + 2}}{{n - 2}}} = 0\)in R n . Arch. Rational Mech. Anal. 122, 159–182 (1993). https://doi.org/10.1007/BF00378166
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00378166