A vector p-Laplacian type approach to multiple periodic solutions for the p-relativistic operator

We prove the existence of at least [Formula: see text] geometrically distinct [Formula: see text]-periodic solutions for a differential inclusions system of the form [Formula: see text] Here, [Formula: see text] is a monotone homeomorphism, [Formula: see text] is periodic with respect to each component of the second variable and [Formula: see text] stands for the generalized Clarke gradient of [Formula: see text] at [Formula: see text]. The monotonicity assumptions on [Formula: see text] highlight the vector [Formula: see text]-Laplacian as being the prototype differential operator. The main interesting feature of this approach is that it also provides a useful framework to treat the case of the [Formula: see text]-relativistic singular operator.