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Existence and uniqueness of positive solution of a logistic equation with nonlinear gradient term

Published online by Cambridge University Press:  12 July 2007

David Ruiz  and
Antonio Suárez
David Ruiz
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain ([email protected])
Antonio Suárez
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Faculdad de Matemáticas, Universidad de Sevilla, C/Tarfia s/n, 41012 Sevilla, Spain ([email protected])
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Abstract

The main goal of this work is to study the existence and uniqueness of a positive solution of a logistic equation including a nonlinear gradient term. In particular, we use local and global bifurcation together with some a priori estimates. To prove uniqueness, the sweeping method of Serrin is employed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 3 , June 2007 , pp. 555 - 566
Copyright
2007 Royal Society of Edinburgh

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