## Differential and Integral Equations

### Structural change of solutions for a scalar curvature equation

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 14, Number 3 (2001), 273-288.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356123328

Mathematical Reviews number (MathSciNet)
MR1799895

Zentralblatt MATH identifier
1016.34024

Subjects
Primary: 34B15: Nonlinear boundary value problems
Secondary: 35B20: Perturbations 35J60: Nonlinear elliptic equations

#### Citation

Morishita, Hiroshi; Yanagida, Eiji; Yotsutani, Shoji. Structural change of solutions for a scalar curvature equation. Differential Integral Equations 14 (2001), no. 3, 273--288. https://projecteuclid.org/euclid.die/1356123328