In this paper we study nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the p...

The general theory of Lyapunov’s stability of first-order differential inclusions in Hilbert spaces has been studied by the authors in a previous work [2]. This new contribution focuses on the natural case when the maximally monotone operator governing the given inclusion has a domain with nonempty interior. This setting permits to have nonincreasing Lyapunov functions on the whole trajectory o...

In this paper, we introduce a new resolvent operator and we call it relaxed resolvent operator. We prove that relaxed resolvent operator is single-valued and Lipschitz continuous and finally we approximate the solution of a variational inclusion problem in Hilbert spaces by defining an iterative algorithm based on relaxed resolvent operator. A few concepts like Lipschitz continuity and strong m...

In this paper, quasi-variational inclusion and fixed point problems are investigated based on a general iterative process. Strong convergence theorems are established in the framework of Hilbert spaces.