Second-order evolution problems by time and state-dependent maximal monotone operators and set-valued perturbations

Document Type : Research Paper


LMPA Laboratory, Department of Mathematics, Mohammed Seddik Benyahia University, Jijel, Algeria


The present work is concerned with a class of perturbed second-order differential inclusions driven by state-dependent maximal monotone operators, in the context of an infinite-dimensional framework. To prove our existence theorem, we make crucial use of a compactness type assumption on the domain of the operators and succeed in adapting to the second-order setting a discretization approach. An application of our main result to the theory of quasi-variational evolution inequalities is provided.


Volume 14, Issue 1
January 2023
Pages 699-715
  • Receive Date: 22 September 2021
  • Revise Date: 24 September 2021
  • Accept Date: 11 September 2022