Differential and Integral Equations

Some mountain-pass solutions for small diffusion

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

In this paper, we considerably improve results of Ni, Takagi, and Wei on the shape of the mountain-pass solution and the location of its maximum for certain boundary-value problems for certain weakly nonlinear elliptic equations with small diffusion, on domains in $\mathbb R^2$ or $\mathbb R^3$. We remove geometric conditions on the domain and nondegeneracy and uniqueness assumptions on the solutions.

Article information

Source
Differential Integral Equations, Volume 16, Number 8 (2003), 1013-1024.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060582

Mathematical Reviews number (MathSciNet)
MR1989600

Zentralblatt MATH identifier
1030.35074

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B25: Singular perturbations 35J20: Variational methods for second-order elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Dancer, E. N. Some mountain-pass solutions for small diffusion. Differential Integral Equations 16 (2003), no. 8, 1013--1024. https://projecteuclid.org/euclid.die/1356060582


Export citation