Electron. J. Diff. Eqns., Vol. 2006(2006), No. 90, pp. 1-21.

Boundary-value problems for Hamiltonian systems and absolute minimizers in calculus of variations

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.

Show me the PDF file (335K), TEX file, and other files for this article.

Vassili N. Kolokol'tsov
Dept of Statistics, University of Warwick
Coventry CV4 7AL, United Kingdom
email: v.kolokoltsov@warwick.ac.uk
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

Return to the EJDE web page