Department of Algebra and Geometry, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic
The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler--Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler--Lagrange equations are found.
AMSclassification. 35A15, 49N60, 58Z05.
Keywords. Euler--Lagrange equations, Hamiltonian systems, Hamilton extremals, Dedecker--Hamilton extremals, Hamilton equations, Lepagean equivalents.