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On a theorem of Picard


Authors: F. Gesztesy and W. Sticka
Journal: Proc. Amer. Math. Soc. 126 (1998), 1089-1099
MSC (1991): Primary 33E05, 34C25; Secondary 58F07
DOI: https://doi.org/10.1090/S0002-9939-98-04668-1
MathSciNet review: 1476130
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Abstract: We extend Picard's theorem on the existence of elliptic solutions of the second kind of linear homogeneous ${n}^{\mathrm{th}}$-order scalar ordinary differential equations with coefficients being elliptic functions (associated with a common period lattice) to linear homogeneous first-order $n\times n$ systems. In particular, the qualitative Floquet-type structure of fundamental systems of solutions in terms of elliptic and exponential functions, polynomials, and Weierstrass zeta functions of the independent variable is determined. Connections with completely integrable systems are mentioned.


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Additional Information

F. Gesztesy
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: fritz@math.missouri.edu

W. Sticka
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211

DOI: https://doi.org/10.1090/S0002-9939-98-04668-1
Received by editor(s): September 23, 1996
Additional Notes: The research was based upon work supported by the National Science Foundation under Grant No. DMS-9623121.
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society

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