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 \(D(A)\neq \mathbb{R}^{N}\) and \(D(A)= \mathbb{R}^{N}\) and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.

中文翻译：

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二阶多值系统的存在性和松弛结果

我们考虑由具有各种边界条件的一般非齐次微分算子驱动的非线性系统，以及具有最大单调项\（A（x）\）和多值摄动\（F（ t，x，y）\），可以是凸值或非凸值。我们考虑\（D（A）\ neq \ mathbb {R} ^ {N} \）和\（D（A）= \ mathbb {R} ^ {N} \）的情况，并证明存在定理和弛豫定理。讨论了微分变分不等式和控制系统的应用。