On an elliptic problem with critical nonlinearity in expanding annuli
This is a continuation of papers by \textit{M. O. Ahmedou} and \textit{K. O. El Mehdi} [Computation of the difference of topology at infinity for Yamabe-type problems on annuli-domains. I, II. Duke Math. J. 94, No. 2, 215-229, 231-255 (1998; Zbl 0966.35043)] in computing the difference of the topology between the level sets caused by the critical points at infinity. The program is initiated by A. Bahri and J. M. Coron in the study of the Kazdan Warner problem in Riemannian geometry. In this paper, the authors study the critical nonlinear elliptic problem on the expanding annuli \(A_\varepsilon= \{x\in \mathbb{R}^n\mid\varepsilon<|x|<{1\over \varepsilon}\}\), and make the above computation for \(\varepsilon\to 0\).
scientific article; zbMATH DE number 1278793