Periodic solutions for nonlinear differential equations with maximal monotone terms Original Research Article

We examine nonlinear periodic problems for scalar and vector differential equations involving a maximal monotone operator which is not necessarily defined everywhere. In the scalar case, the nonlinear differential operator depends on both x and x′, linearly in x′, while in the vector case the differential operator depends only on x′ and is a generalization of the p-Laplacian. Our approach is based on the theory of operators of monotone type and on the Leray–Schauder principle.