Open Access
2003 Some mountain-pass solutions for small diffusion
E. N. Dancer
Differential Integral Equations 16(8): 1013-1024 (2003). DOI: 10.57262/die/1356060582


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.


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E. N. Dancer. "Some mountain-pass solutions for small diffusion." Differential Integral Equations 16 (8) 1013 - 1024, 2003.


Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1030.35074
MathSciNet: MR1989600
Digital Object Identifier: 10.57262/die/1356060582

Primary: 35J60
Secondary: 35B25 , 35J20 , 58E05

Rights: Copyright © 2003 Khayyam Publishing, Inc.

Vol.16 • No. 8 • 2003
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