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Some remarks on a Neumann boundary value problem arising in fluid dynamics

Published online by Cambridge University Press:  17 February 2009

Pedro J. Torres
Pedro J. Torres
Affiliation:
Dep. de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain; e-mail: [email protected].
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Abstract

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It is proved that the Neumann boundary value problem, which Mays and Norbury have recently connected with a certain fluid dynamics equation, has a positive solution for any positive value of a particular parameter. Uniform bounds for the solutions and symmetry on a given range of the parameter are also introduced. The proofs include Krasnoselskii's classical fixed-point theorem on cones of a Banach space and basic comparison techniques.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 3 , January 2004 , pp. 327 - 332
Copyright
Copyright © Australian Mathematical Society 2004

References

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[3]Mays, L. and Norbury, J., “Bifurcation of positive solutions for a Neumann boundary value problem”, ANZIAM J. 42 (2001) 324–340.CrossRefGoogle Scholar
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