Differential equations with a given set of solutions

Jaume Llibre; Rafael Ramírez; Natalia Sadovskaia

doi:10.1016/j.amc.2019.124659

Differential equations with a given set of solutions

Jaume Llibre, Rafael Ramírez, Natalia Sadovskaia

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© 2019 Elsevier Inc. The aim of this paper is to study the following inverse problem of ordinary differential equations: For a given set of analytic functions ω={z1(t),…,zr(t)}, with zj(t)=xj(t)+iyj(t) and z¯j(t)=xj(t)−iyj(t) for j=1,…,r, defined in the open interval I⊆R, we want to determine the differential equation F(t,z¯,z,z˙,z¯˙,…,z(n),z¯(n))=0,where [Formula presented] for j=1,…,n, in such a way that the given set of functions ω is a set of solutions of this differential equation.

Original language	English
Article number	124659
Number of pages	20
Journal	Applied Mathematics and Computation
Volume	365
DOIs	https://doi.org/10.1016/j.amc.2019.124659
Publication status	Published - 15 Jan 2020

Keywords

16TH HILBERT PROBLEM
Abel equation
First integral
INVERSE APPROACH
Inverse problem for ordinary differential equations
Planar differential system
Ricatti equation

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10.1016/j.amc.2019.124659

https://ddd.uab.cat/record/221355Licence: CC BY-NC-ND

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title = "Differential equations with a given set of solutions",

abstract = "{\textcopyright} 2019 Elsevier Inc. The aim of this paper is to study the following inverse problem of ordinary differential equations: For a given set of analytic functions ω={z1(t),…,zr(t)}, with zj(t)=xj(t)+iyj(t) and z¯j(t)=xj(t)−iyj(t) for j=1,…,r, defined in the open interval I⊆R, we want to determine the differential equation F(t,z¯,z,z˙,z¯˙,…,z(n),z¯(n))=0,where [Formula presented] for j=1,…,n, in such a way that the given set of functions ω is a set of solutions of this differential equation.",

keywords = "16TH HILBERT PROBLEM, Abel equation, First integral, INVERSE APPROACH, Inverse problem for ordinary differential equations, Planar differential system, Ricatti equation",

author = "Jaume Llibre and Rafael Ram{\'i}rez and Natalia Sadovskaia",

year = "2020",

month = jan,

day = "15",

doi = "10.1016/j.amc.2019.124659",

language = "English",

volume = "365",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

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TY - JOUR

T1 - Differential equations with a given set of solutions

AU - Llibre, Jaume

AU - Ramírez, Rafael

AU - Sadovskaia, Natalia

PY - 2020/1/15

Y1 - 2020/1/15

N2 - © 2019 Elsevier Inc. The aim of this paper is to study the following inverse problem of ordinary differential equations: For a given set of analytic functions ω={z1(t),…,zr(t)}, with zj(t)=xj(t)+iyj(t) and z¯j(t)=xj(t)−iyj(t) for j=1,…,r, defined in the open interval I⊆R, we want to determine the differential equation F(t,z¯,z,z˙,z¯˙,…,z(n),z¯(n))=0,where [Formula presented] for j=1,…,n, in such a way that the given set of functions ω is a set of solutions of this differential equation.

AB - © 2019 Elsevier Inc. The aim of this paper is to study the following inverse problem of ordinary differential equations: For a given set of analytic functions ω={z1(t),…,zr(t)}, with zj(t)=xj(t)+iyj(t) and z¯j(t)=xj(t)−iyj(t) for j=1,…,r, defined in the open interval I⊆R, we want to determine the differential equation F(t,z¯,z,z˙,z¯˙,…,z(n),z¯(n))=0,where [Formula presented] for j=1,…,n, in such a way that the given set of functions ω is a set of solutions of this differential equation.

KW - 16TH HILBERT PROBLEM

KW - Abel equation

KW - First integral

KW - INVERSE APPROACH

KW - Inverse problem for ordinary differential equations

KW - Planar differential system

KW - Ricatti equation

UR - http://www.mendeley.com/catalogue/differential-equations-given-set-solutions

U2 - 10.1016/j.amc.2019.124659

DO - 10.1016/j.amc.2019.124659

M3 - Article

SN - 0096-3003

VL - 365

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 124659

ER -

Differential equations with a given set of solutions

Abstract

Keywords

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