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H. Berestycki & L. Nirenberg, Monotonicty, symmetry and anti-symmetry of solutions of semilinear elliptic equations, J. Geometry Physics 5 (1988), 237–275.
H. Berestycki & L. Nirenberg, Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains, Analysis, et Cetera: Research papers published in honor of Jürgen Moser (P. H. Rabinowitz & E. Zehnder, Eds.), Academic Press, 1990, 115–164.
L. Caffarelli, B. Gidas & J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989), 271–297.
W. Chen & C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), 615–622.
B. Franchi & E. Lanconelli, Radial symmetry of the ground states for a class of quasilinear elliptic equations, Nonlinear Diffusion Equations and Their Equilibrium States (W.-M. Ni, L. A. Peletier & J. Serrin, Eds.), Vol. 1 (1988), 287–292.
B. Gidas, W.-M. Ni & L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in R n, Advances in Math. Supplementary Studies 7 A (L. Nachbin Ed.), (1981) 369–402.
D. Gilbarg & N. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag, 1983.
Y. Li & W.-M. Ni, On conformal scalar curvature equations in R n,Duke Math J. 57 (1988), 895–924.
Y. Li & W.-M. Ni, On the existence and symmetry properties of finite total mass solutions of the Matukuma equation, the Eddington equation and their generalizations, Arch. Rational Mech. Anal. 108 (1989), 175–194.
W.-M. Ni, On the elliptic equation \(\Delta u + K(x)u^{\tfrac{{n + 2}}{{n - 2}}} = 0\), its generalizations and applications in geometry, Indiana Univ. Math. J. 31 (1982), 493–529.
E. Yanagida, Structure of positive radial solutions of Matukuma's equation, Japan J. Indust. Appl. Math. 8 (1991), 165–173.
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Li, Y., Ni, W.M. On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in R n II. Radial symmetry. Arch. Rational Mech. Anal. 118, 223–243 (1992). https://doi.org/10.1007/BF00387896
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DOI: https://doi.org/10.1007/BF00387896