Vassili N. Kolokol'tsov, Alexey E. Tyukov
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
| Alexey E. Tyukov |
Cardiff School of Mathematics, Cardiff University
Senghennydd Road, Cardiff, CF24 4AG, United Kingdom
email: tyukovA@cardiff.ac.uk firstname.lastname@example.org
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