## Differential and Integral Equations

### Stable solutions on $\R^n$ and the primary branch of some non-self-adjoint convex problems

E. N. Dancer

#### Abstract

We prove that if $n = 2$ or $3$, the problem $- \Delta u = e^u$ on $R^n$ has no stable negative solution. We then use this to remove self-adjointness conditions in a paper of Crandall and Rabinowitz on the primary branch of positive solutions of a nonlinear boundary-value problem.

#### Article information

Source
Differential Integral Equations Volume 17, Number 9-10 (2004), 961-970.

Dates
First available in Project Euclid: 21 December 2012

Dancer, E. N. Stable solutions on $\R^n$ and the primary branch of some non-self-adjoint convex problems. Differential Integral Equations 17 (2004), no. 9-10, 961--970.https://projecteuclid.org/euclid.die/1356060309