A Note on Linear Differential Equations with Periodic Coefficients Articles uri icon

authors

  • PERALTA SALAS, DANIEL
  • Grau, Maite

publication date

  • October 2009

start page

  • 3197

end page

  • 3202

issue

  • 7-8

volume

  • 71

International Standard Serial Number (ISSN)

  • 0362-546X

Electronic International Standard Serial Number (EISSN)

  • 1873-5215

abstract

  • We consider linear homogeneous differential equations of the form x = A(t)x where A (t) is a square matrix of C1, real and T -periodic functions, with T > 0. We give several criteria on the matrix A(t) to prove the asymptotic stability of the trivial solution to equation x = A(t)x. These criteria allow us to show that any finite configuration of cycles in Rn can be realized as hyperbolic limit cycles of a polynomial vector field