Structural change of solutions for a scalar curvature equation
In the case that \(p= n+ 2/n-2\) and \(n> 2\), \textit{W. Ding} and \textit{W. Ni} [Duke Math. J. 52, 485-506 (1985; Zbl 0592.35048)] showed that the structure of radial solutions to the scalar curvature equation \[ \Delta u+ \{1+\varepsilon k(|x|)\} u^p= 0,\quad x\in \mathbb{R}^n, \] drastically changes under the perturbation \(\varepsilon k(|x|)\). Motivated by the above work, the authors show that such a structure changes can be understood in a natural way if \(p\) is also taken as a parameter and \(k\) satisfies some suitable conditions. The Pohozaev identity plays an important role in the perturbation analysis.
scientific article; zbMATH DE number 1832819