Differential and Integral Equations

Asymptotic behavior of positive solutions of quasilinear elliptic equations with critical Sobolev growth

Emmanuel Hebey

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Abstract

In this short note we investigate the asymptotic behavior of positive minimizing solutions $u_\epsilon$ to the equation $\Delta u_\epsilon = N(N-2) f(x) u_\epsilon^{p-\epsilon}$ in $\Omega$ and $u_\epsilon = 0$ on $\partial\Omega$, where $\Delta$ stands for the Euclidean Laplacian with the minus sign convention, $\Omega$ is a smooth bounded domain in ${\mathbb R}^N$, $p = (N+2)/(N-2)$ is the critical Sobolev exponent, and $f$ belongs to a fairly general class of functions.

Article information

Source
Differential Integral Equations Volume 13, Number 7-9 (2000), 1073-1080.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061210

Mathematical Reviews number (MathSciNet)
MR1775246

Zentralblatt MATH identifier
0976.35022

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B40: Asymptotic behavior of solutions 35J20: Variational methods for second-order elliptic equations

Citation

Hebey, Emmanuel. Asymptotic behavior of positive solutions of quasilinear elliptic equations with critical Sobolev growth. Differential Integral Equations 13 (2000), no. 7-9, 1073--1080. https://projecteuclid.org/euclid.die/1356061210.


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