96-319 F. Gesztesy and W. Sticka

On a Theorem of Picard (41K, Latex) Jun 26, 96

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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

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