AbstractWe consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term $A(x)$
A
(
x
)
and of a multivalued perturbation $F(t,x,y)$
F
(
t
,
x
,
y
)
which can be convex or nonconvex valued. We consider the cases where $D(A)\neq \mathbb{R}^{N}$
D
(
A
)
≠
R
N
and $D(A)= \mathbb{R}^{N}$
D
(
A
)
=
R
N
and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.
Existence and Relaxation Results for Second Order Multivalued Systems