Showing items related by title, author, creator and subject.

• Polynomial and rational first integrals for planar homogeneous polynomial differential systems 

  Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (Universitat Autònoma de Barcelona, 2014)

  In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic ...

• Integrability of planar polynomial differential systems through linear differential equations 

  Giacomini, Héctor; Giné, Jaume; Grau Montaña, Maite (Rocky Mountain Mathematics Consortium, 2006)

  In this work we consider rational ordinary differential equations dy/dx = Q(x, y)/P(x, y), with Q(x, y) and P(x, y) coprime polynomials with real coefficients. We give a method to construct equations of this type for ...

• Centers for the Kukles homogeneous systems with even degree 

  Giné, Jaume; Llibre, Jaume; Valls, Claudia (Shanghai Normal University & Wilmington Scientific Publisher, 2017)

  For the polynomial differential system x˙=−y, y˙=x+Qn(x,y), where Qn(x,y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for n≥2 has a ...