Differential and Integral Equations

Asymptotic behavior and uniqueness results for boundary blow-up solutions

Yihong Du

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Abstract

We estimate the blow-up rate and then improve some existing uniqueness results for boundary blow-up solutions to certain quasilinear elliptic equations with a weight function. The weight function is allowed to vanish on the part of the boundary where the solution blows up. Our approach is based on the construction of certain upper and lower solutions on small annuli with partial boundary blow-up, and on a modified version of an iteration technique due to Safonov.

Article information

Source
Differential Integral Equations Volume 17, Number 7-8 (2004), 819-834.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060331

Mathematical Reviews number (MathSciNet)
MR2074688

Zentralblatt MATH identifier
1150.35369

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B40: Asymptotic behavior of solutions 35B50: Maximum principles 92D25: Population dynamics (general)

Citation

Du, Yihong. Asymptotic behavior and uniqueness results for boundary blow-up solutions. Differential Integral Equations 17 (2004), no. 7-8, 819--834. https://projecteuclid.org/euclid.die/1356060331.


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