Darboux integrating factors Inverse problems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Christopher, Colin³  Llibre, Jaume⁴  Pantazi, Chara¹  Walcher, Sebastian² 

[1] Univ Politecn Cataluna, Dept Matemat Aplicada 1, EPSEB, E-08028 Barcelona, Spain

[2] Rhein Westfal TH Aachen, Lehrstuhl Math A, D-52056 Aachen, Germany

[3] Univ Plymouth, Dept Math & Stat, Plymouth PL3 3AJ, Devon, England

[4] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

关键词: Polynomial differential system;    Invariant algebraic curve;    Integrating factor;   

DOI  :  10.1016/j.jde.2010.10.013

来源: Elsevier

【 摘 要 】

We discuss planar polynomial vector fields with prescribed Darboux integrating factors in a nondegenerate affine geometric setting We establish a reduction principle which transfers the problem to polynomial solutions of certain meromorphic linear systems and show that the space of vector fields with a given integrating factor modulo a subspace of explicitly known standard vector fields has finite dimension For several classes of examples we determine this space explicitly (C) 2010 Elsevier Inc All rights reserved

【 授权许可】

Free