Differential and Integral Equations

Bounded positive solutions of rotationally symmetric harmonic map equations

Leung-Fu Cheung, Chun-Kong Law, and Man-Chun Leung

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Abstract

We consider bounded positive solutions $\alpha$ of rotationally symmetric harmonic map equations. We study the continuity of the maps $\alpha' (0) \mapsto \alpha (\infty)$ and $\alpha (1) \mapsto \alpha (\infty)$ in connection with the Dirichlet problem at infinity. Regularity at zero, local properties and conditions for positive solutions to be blowing up, unbounded, or bounded are discussed.

Article information

Source
Differential Integral Equations Volume 13, Number 7-9 (2000), 1149-1188.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061215

Mathematical Reviews number (MathSciNet)
MR1775251

Zentralblatt MATH identifier
0984.34018

Subjects
Primary: 34B18: Positive solutions of nonlinear boundary value problems
Secondary: 35A30: Geometric theory, characteristics, transformations [See also 58J70, 58J72] 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 58E20: Harmonic maps [See also 53C43], etc.

Citation

Cheung, Leung-Fu; Law, Chun-Kong; Leung, Man-Chun. Bounded positive solutions of rotationally symmetric harmonic map equations. Differential Integral Equations 13 (2000), no. 7-9, 1149--1188. https://projecteuclid.org/euclid.die/1356061215.


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