F. Gesztesy and W. Sticka
On a Theorem of Picard
(41K, Latex)
ABSTRACT. We extend Picard's theorem on the existence of elliptic solutions of the
second kind of linear homogeneous n-th order scalar differential
equations with coefficients being elliptic functions to linear
homogeneous first-order n x n systems. In particular, the qualitative
structure of the general solution in terms of elliptic and exponential
functions, polynomials, and Weierstrass zeta functions of the independent
variable is determined. Connections with completely integrable
systems are also mentioned