Differential and Integral Equations

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

E. N. Dancer

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

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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060309

Mathematical Reviews number (MathSciNet)
MR2082455

Zentralblatt MATH identifier
1150.35357

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25]

Citation

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.


Export citation