Let (P, Q) be a C1 vector field defined in an open subset U IR2. We call inverse integrating factor a C1 solution V(x, y) of the equation . In previous works it has been shown that this function plays an important ro...Let (P, Q) be a C1 vector field defined in an open subset U IR2. We call inverse integrating factor a C1 solution V(x, y) of the equation . In previous works it has been shown that this function plays an important role in the problem of the center and in the determination of limit cycles. In this paper we obtain necessary conditions for a polynomial vector field (P, Q) to have a polynomial inverse integrating factor.展开更多
We characterize the complex differential equations of the form dy/dx=a_(n)(x)y^)n_+a_(n-1)(x)y^(n-1)+…+a_(1)(x)y+a_(0)(x) where a_(j)(x) are meromorphic functions in the variable x for j = 0,..., n that admit either ...We characterize the complex differential equations of the form dy/dx=a_(n)(x)y^)n_+a_(n-1)(x)y^(n-1)+…+a_(1)(x)y+a_(0)(x) where a_(j)(x) are meromorphic functions in the variable x for j = 0,..., n that admit either a Weierstrass first integral or a Weierstrass inverse integrating factor.展开更多
基金the DGICYT grant, number PB96-1153 The third author is partially supported by the University of Lleida Project P98-207.
文摘Let (P, Q) be a C1 vector field defined in an open subset U IR2. We call inverse integrating factor a C1 solution V(x, y) of the equation . In previous works it has been shown that this function plays an important role in the problem of the center and in the determination of limit cycles. In this paper we obtain necessary conditions for a polynomial vector field (P, Q) to have a polynomial inverse integrating factor.
基金partially supported by the Ministerio de Economia,Industria y Competitividad,Agencia Estatal de Investigacion grant MTM2016-77278-P (FEDER)the Agència de Gestio d’Ajuts Universitaris i de Recerca grant 2017SGR1617+1 种基金the H2020 European Research Council grant MSCA-RISE-2017-777911partially supported by FCT/Portugal through the pro ject UID/MAT/04459/2013。
文摘We characterize the complex differential equations of the form dy/dx=a_(n)(x)y^)n_+a_(n-1)(x)y^(n-1)+…+a_(1)(x)y+a_(0)(x) where a_(j)(x) are meromorphic functions in the variable x for j = 0,..., n that admit either a Weierstrass first integral or a Weierstrass inverse integrating factor.
