Differential and Integral Equations

Some mountain-pass solutions for small diffusion

E. N. Dancer

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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.)


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

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