Abstract
We will consider radial solutions of the following problem: where, ϕ is a continuous radial function and ɛ is a small real parameter. This equation and its generalizations have been studied in a large numbers of papers (see for example [BE], [DN], [LN], [NI1&2]).
Supported by a CNR fellowship
Supported in part by NSF Grant DMS-8914778
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References
F.V. Atkinson, L.A. Peletier, Emden-Fowler Equations Involving Critical Exponents. Nonlinear Analysis T.M.A. 10 (1986), 755–766.
A. Bahri, J.-M. Coron, The Scalar-Curvature Problem on the Standard three-dimensional Sphere. To appear in J. Funct. Anal..
G. Bianchi, H. Egnell, work in progress.
A. Chang, P. Yang, work in progress.
W.-Y. Ding, Unpublished work.
W.-Y. Ding, W.-M. Ni, On the Elliptic Equation and Related Topics. Duke Math. J. 52 (1985), 485–486.
H. Egnell, I. Kaj, Positive Global Solutions of a Nonhomogeneous Semilinear Elliptic Equation. To appear in J. Math. Pure Appl..
J. Escobar, R. Schoen, Conformai Metrics with Prescribed Scalar Curvature. Invent. Math. 86 (1986), 243–254.
J. Kazdan, F. Warner, Existence and Conformai Deformations of Metrics with Prescribed Gaussian and Scalar Curvature. Ann. of Math. 101 (1975), 317–331.
Y. Li, W.-M. Ni, On the Conformai Scalar Curvature in R n. Duke Math. J. 57 (1988), 895–924.
W.-M. Ni, On the Elliptic Equation, its Generalizations, and Applications in Geometry. Indiana Univ. Math. J. 31 (1982), 493–529.
W.-M. Ni, Some Aspects of Semilinear Elliptic Equations on R n. Nonlinear Diffusion Equations and Their Equilibrium States II, 171–205. Ed. W.-M. Ni. Springer Verlag (1988).
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Bianchi, G., Egnell, H. (1992). Local Existence and Uniqueness of Positive Solutions of the Equation \(\Delta u + \left( {1 + \varepsilon \varphi \left( r \right)} \right){u^{\tfrac{{n + 2}}{{n - 2}}}} = 0\), in ℝn and a Related Equation. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_8
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DOI: https://doi.org/10.1007/978-1-4612-0393-3_8
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