Abstract
We consider a perturbed hemivariational inequality with an additional negative subdifferential term and history-dependent operators. The perturbation is represented by a multivalued mapping, and its values are not assumed to be convex or bounded. We prove that there is a solution to our problem and establish a relaxation-approximation result for it using a localized version of Hausdorff-Lipschitz continuity adapted to the unbounded case.
| Original language | English |
|---|---|
| Pages (from-to) | 545-564 |
| Number of pages | 20 |
| Journal | Journal of Convex Analysis |
| Volume | 35 |
| Issue number | 2 |
| Publication status | Published - 2025 |
Keywords
- difference of subdifferentials
- hemivariational inequality
- history-dependent operators
- truncated Lipschitz condition
- Unbounded perturbation