Vassili N. Kolokol'tsov, Alexey E. Tyukov
Abstract:
We apply the method of Hamilton shooting to obtain the
well-posedness of boundary value problems for certain Hamiltonian
systems and some estimates for their solutions. The examples of
Hamiltonian functions covered by the method include elliptic
polynomials and exponentially growing functions. As a consequence we
prove global existence, smoothness and almost everywhere uniqueness
of absolute minimizers in the corresponding problem of calculus of
variations and hence construct the global field of extremals.
Submitted November 14, 2005. Published August 15, 2006.
Math Subject Classifications: 49J99, 34B15.
Key Words: Hamiltonian systems; absolute minimizers;
global field of extremals; WKB method.
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Vassili N. Kolokol'tsov Dept of Statistics, University of Warwick Coventry CV4 7AL, United Kingdom email: v.kolokoltsov@warwick.ac.uk |
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Alexey E. Tyukov Cardiff School of Mathematics, Cardiff University Senghennydd Road, Cardiff, CF24 4AG, United Kingdom email: tyukovA@cardiff.ac.uk tyukov@yahoo.co.uk |
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