Differential and Integral Equations

Structural change of solutions for a scalar curvature equation

Hiroshi Morishita, Eiji Yanagida, and Shoji Yotsutani

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation