An <mml:math alttext="$H$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>H</mml:mi></mml:math>-system for a revolution surface without boundary

Amster, P.; De Nápoli, P.; Mariani, M. C.

doi:https://doi.org/10.1155/AAA/2006/93163

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Volume 2006 | Article ID 093163 | https://doi.org/10.1155/AAA/2006/93163

An H-system for a revolution surface without boundary

P. Amster,^1,2P. De Nápoli,^1,2and M. C. Mariani³

Received20 Nov 2003

Accepted25 Apr 2005

Published07 Mar 2006

Abstract

We study the existence of solutions an H-system for a revolution surface without boundary for H depending on the radius f. Under suitable conditions we prove that the existence of a solution is equivalent to the solvability of a scalar equation N(a)=L/2, where N:𝒜⊂ℝ+→ℝ is a function depending on H. Moreover, using the method of upper and lower solutions we prove existence results for some particular examples. In particular, applying a diagonal argument we prove the existence of unbounded surfaces with prescribed H.

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Copyright

Copyright © 2006 P. Amster et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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