Differential equations with a given set of solutions

Jaume Llibre, Rafael Ramírez, Natalia Sadovskaia

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Article number124659
Number of pages20
JournalApplied Mathematics and Computation
Volume365
DOIs
Publication statusPublished - 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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