Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T08:40:05.991Z Has data issue: false hasContentIssue false
  • English
  • Français

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].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Benjamin, T. B., “A new kind of solitary wave”, J. Fluid Mech. 245 (1992) 401–411.CrossRefGoogle Scholar
[2]Krasnosel'skii, M. A., Positive solutions of operator equations (Nordhoff, Groningen, 1964).Google Scholar
[3]Mays, L. and Norbury, J., “Bifurcation of positive solutions for a Neumann boundary value problem”, ANZIAM J. 42 (2001) 324–340.CrossRefGoogle Scholar
[4]Merivenci Atici, F. and Guseinov, G. Sh., “On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions”, J. Comp. Appl. Math. 132 (2001) 341–356.CrossRefGoogle Scholar