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A problem in non-linear Diophantine approximation

Harrap, S.; Hussain, M.; Kristensen, S.

A problem in non-linear Diophantine approximation Thumbnail


M. Hussain

S. Kristensen


In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.


Harrap, S., Hussain, M., & Kristensen, S. (2018). A problem in non-linear Diophantine approximation. Nonlinearity, 31(5), 1734-1756.

Journal Article Type Article
Acceptance Date Jan 2, 2018
Online Publication Date Mar 27, 2018
Publication Date May 1, 2018
Deposit Date Dec 30, 2015
Publicly Available Date Mar 27, 2019
Journal Nonlinearity
Print ISSN 0951-7715
Electronic ISSN 1361-6544
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 31
Issue 5
Pages 1734-1756
Related Public URLs


Accepted Journal Article (344 Kb)

Copyright Statement
This is an author-created, un-copyedited version of an article accepted for publication/published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at

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