  We study optimality conditions for various types of control problems like the
standard optimal control problem, optimal multiprocesses, problems with
infinite horizon or the control of Volterra integral equations. To derive
necessary conditions the needle variation method of Ioffe & Tichomirov is the
central tool. In the particular control problem with infinite horizon the
question of a suitable setting arises. We propose the framework of continuous
state trajectories converging at infinity. This requires a version of Riesz'
representation theorem and the introduction of regular Borel measures on the
extended real number line. The control of Volterra integral equations including
an inner and outer time variable. Consequently, we deal with a two-dimensional
time set. We extend the needle variation method of Ioffe & Tichomirov to this
case. The obtained optimality conditions are demonstrated in illustrative
examples.
