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Some remarks on a Neumann boundary value problem arising in fluid dynamics. (English) Zbl 1053.34019

The aim of this paper is to confirm and to complete by analytical methods some results obtained by L. Mays and J. Norbury [ANZIAM J. 42, No. 3, 324–340 (2001; Zbl 0980.34018)] for a Neumann boundary value problem arising in fluid dynamics. They have used analytical approximation and numerical methods to solve this problem. In particular, the author gives uniform bounds for the solutions if the parameter belongs to some interval.
Kranoselskii’s classical fixed-point theorem on cones of a Banach space and comparison techniques are used.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations

Citations:

Zbl 0980.34018
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Full Text: DOI

References:

[1] DOI: 10.1016/S0377-0427(00)00438-6 · Zbl 0993.34022 · doi:10.1016/S0377-0427(00)00438-6
[2] DOI: 10.1017/S002211209200051X · Zbl 0779.76013 · doi:10.1017/S002211209200051X
[3] Krasnosel’skii, Positive solutions of operator equations (1964)
[4] Mays, ANZIAM J. 42 pp 324– (2001)
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