## A problem in non-linear Diophantine approximation

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### Standard

A problem in non-linear Diophantine approximation. / Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon.

I: Nonlinearity, Bind 31, Nr. 5, 27.03.2018, s. 1734-1756.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

### Harvard

Harrap, S, Hussain, M & Kristensen, S 2018, 'A problem in non-linear Diophantine approximation', Nonlinearity, bind 31, nr. 5, s. 1734-1756. https://doi.org/10.1088/1361-6544/aaa498

### MLA

Harrap, Stephen, Mumtaz Hussain, og Simon Kristensen. "A problem in non-linear Diophantine approximation". Nonlinearity. 2018, 31(5). 1734-1756. https://doi.org/10.1088/1361-6544/aaa498

### Author

Harrap, Stephen ; Hussain, Mumtaz ; Kristensen, Simon. / A problem in non-linear Diophantine approximation. I: Nonlinearity. 2018 ; Bind 31, Nr. 5. s. 1734-1756.

### Bibtex

@article{2da72a163c5b41e889f9a201b600d771,
title = "A problem in non-linear Diophantine approximation",
abstract = "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.",
keywords = "Hausdorff dimension, Hausdorff measure, Khintchine-Groshev theorem, non-linear Diophantine approximation, partial differential equations",
author = "Stephen Harrap and Mumtaz Hussain and Simon Kristensen",
year = "2018",
month = mar,
day = "27",
doi = "10.1088/1361-6544/aaa498",
language = "English",
volume = "31",
pages = "1734--1756",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "Institute of Physics Publishing Ltd.",
number = "5",

}

### RIS

TY - JOUR

T1 - A problem in non-linear Diophantine approximation

AU - Harrap, Stephen

AU - Hussain, Mumtaz

AU - Kristensen, Simon

PY - 2018/3/27

Y1 - 2018/3/27

N2 - 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.

AB - 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.

KW - Hausdorff dimension

KW - Hausdorff measure

KW - Khintchine-Groshev theorem

KW - non-linear Diophantine approximation

KW - partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=85045661029&partnerID=8YFLogxK

U2 - 10.1088/1361-6544/aaa498

DO - 10.1088/1361-6544/aaa498

M3 - Journal article

AN - SCOPUS:85045661029

VL - 31

SP - 1734

EP - 1756

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 5

ER -