On a theorem of Picard
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- by F. Gesztesy and W. Sticka PDF
- Proc. Amer. Math. Soc. 126 (1998), 1089-1099 Request permission
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.References
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Additional Information
- F. Gesztesy
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 72880
- Email: fritz@math.missouri.edu
- W. Sticka
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- 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
- © Copyright 1998 American Mathematical Society
- 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