Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 90, pp. 1-21.

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

Authors: Vassili N. Kolokol'tsov (Univ. of Warwick, UK)
         Alexey E. Tyukov (Cardiff Univ., UK)
	 
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.