We 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) and of a multivalued perturbation F(t, x, y) which can be convex or nonconvex valued. We consider the cases where D(A) ≠ RN and D(A) = RN and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.
Papageorgiou N.S., Vetro C. (2021). Existence and Relaxation Results for Second Order Multivalued Systems. ACTA APPLICANDAE MATHEMATICAE, 173(1), 1-36 [10.1007/s10440-021-00410-9].
Existence and Relaxation Results for Second Order Multivalued Systems
Vetro C.
2021-01-01
Abstract
We 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) and of a multivalued perturbation F(t, x, y) which can be convex or nonconvex valued. We consider the cases where D(A) ≠ RN and D(A) = RN and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.
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