  This paper investigates the necessary conditions of optimality for uni-
formly overtaking optimal control on infinite horizon with free right endpoint.
Clarke's form of the Pontryagin Maximum Principle is proved without the as-
sumption on boundedness of total variation of adjoint variable. The
transversality condition for adjoint variable is shown to become necessary if
the adjoint variable is partially Lyapunov stable. The modifications of this
condition are proposed for the case of unbounded adjoint variable. The
Cauchy-type formula for the adjoint variable proposed by S. M. Aseev and A. V.
Kryazhimskii is shown to complement relations of the Pontryagin Maximum
Principle up to the complete set of necessary conditions of optimality if the
improper integral in the formula converges conditionally and continuously
depends on the original position. The results are extended to an unbounded
objective functional (described by a non- convergent improper integral),
unbounded constraint on the control, and uniformly sporadically catching up
optimal control.
