  We provide an extension of the Hartman-Knobloch theorem for periodic
solutions of vector differential systems to a general class of $\phi$-Laplacian
differential operators. Our main tool is a variant of the Man\'{a}sevich-Mawhin
continuation theorem developed for this class of operator equations, together
with the theory of bound sets. Our results concern the case of convex bound
sets for which we show some new connections using a characterisation of
sublevel sets due to Krantz and Parks. We also extend to the $\phi$-Laplacian
vector case a classical theorem of Reissig for scalar periodically perturbed
Li\'{e}nard equations.
