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We provide an extension of the Hartman-Knobloch theorem for periodicsolutions of vector differential systems to a general class of $\phi$-Laplaciandifferential operators. Our main tool is a variant of the Man\'{a}sevich-Mawhincontinuation theorem developed for this class of operator equations, togetherwith the theory of bound sets. Our results concern the case of convex boundsets for which we show some new connections using a characterisation ofsublevel sets due to Krantz and Parks. We also extend to the $\phi$-Laplacianvector case a classical theorem of Reissig for scalar periodically perturbedLi\'{e}nard equations.

Bound sets for a class of $\phi$-Laplacian operators