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2008 Local property of the mountain-pass critical point and the mean field equation
Hiroshi Ohtsuka, Takashi Suzuki
Differential Integral Equations 21(5-6): 421-432 (2008). DOI: 10.57262/die/1356038625


A local property of the mountain-pass critical point obtained by Struwe's monotonicity trick is shown. Given one parameter family of functionals $\{ I_\lambda\}$ provided with the structural assumption of monotonicity, we assume that each $I_\lambda$ satisfies the bounded Palais-Smale condition, its mountain-pass critical value $c_{\lambda}$ is differentiable at $\lambda=\lambda_0$, and $\mbox{Cr}(I, c_{\lambda_0})=\{v\mid I'_{\lambda_0}(v)=0, \ I_{\lambda_0}(v)=c_{\lambda_0} \}$ is compact. Then, there is $v\in \mbox{Cr}(I, c_{\lambda_0})$, either a local minimum or of mountain pass type. Application to the mean field equation is provided.


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Hiroshi Ohtsuka. Takashi Suzuki. "Local property of the mountain-pass critical point and the mean field equation." Differential Integral Equations 21 (5-6) 421 - 432, 2008.


Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35086
MathSciNet: MR2483261
Digital Object Identifier: 10.57262/die/1356038625

Primary: 35J60
Secondary: 35J20 , 47J30 , 49J35

Rights: Copyright © 2008 Khayyam Publishing, Inc.

Vol.21 • No. 5-6 • 2008
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