STRONGLY NONLINEAR, MULTIVALUED, PERIODIC PROBLEMS WITH MAXIMAL MONOTONE TERMS

In this paper we study periodic, nonlinear, second-order differential inclusions, driven by the differential operator x -> (alpha(x)vertical bar vertical bar x'vertical bar vertical bar(p-2)x')' and involving a maximal monotone term A and a multivalued nonlinearity F (t, x) which satisfies the Hartman condition. We do not assume that domA is all of R-N, and so our formulation incorporates variational inequalities. Then we obtain partial generalizations. First, we allow F to depend on x' but for p = 2 and for the scalar problem (N = 1). Second, we assume a general multivalued, nonlinear differential operator x -> alpha(x, x')'; the nonlinearity F depends also on x', but the boundary conditions are Dirichlet. Our methods are based on notions and techniques from multivalued analysis and from the theory of operators of monotone type.