  We investigate necessary conditions of optimality for the Bolza-type infinite
horizon problem with free right end. The optimality is understood in the sense
of weakly uniformly overtaking optimal control. No previous knowledge in the
asymptotic behaviour of trajectories or adjoint variables is necessary.
Following Seierstad's idea, we obtain the necessary boundary condition at
infinity in the form of a transversality condition for the maximum principle.
Those transversality conditions may be expressed in the integral form through
an Aseev--Kryazhimskii-type formulae for co-state arcs. The connection between
these formulae and limiting gradients of payoff function at infinity is
identified; several conditions under which it is possible to explicitly specify
the co-state arc through those Aseev--Kryazhimskii-type formulae are found. For
infinite horizon problem of Bolza type, an example is given to clarify the use
of the Aseev--Kryazhimskii formula as explicit expression of the co-state arc.
