Abstract
A semilinear elliptic equation \[ \Delta u + \{1 + {\varepsilon} k(|x|) \} u^p=0, \quad x \in {\bf R}^n, \] is studied, where $n>2$ and ${\varepsilon}$ is a small parameter. It is known that for $p=(n+2)/(n-2)$ fixed, the structure of radial solutions drastically changes under the perturbation ${\varepsilon} k(|x|)$. In this paper it is shown that such a structural change can be understood in a natural way if the exponent $p$ also is taken as a parameter. The Pohozaev identity plays an important role in the perturbation analysis.
Citation
Hiroshi Morishita. Eiji Yanagida. Shoji Yotsutani. "Structural change of solutions for a scalar curvature equation." Differential Integral Equations 14 (3) 273 - 288, 2001. https://doi.org/10.57262/die/1356123328
Information