# Nonlinear second order evolution inclusions with noncoercive viscosity term

## TL;DR

This paper proves the existence of solutions for a second order nonlinear evolution inclusion with a noncoercive viscosity term using regularization and a priori bounds.

## Contribution

It introduces a novel approach to handle noncoercive viscosity terms in second order evolution inclusions through regularization and limit processes.

## Key findings

- Existence of solutions established for the nonlinear evolution inclusion.
- Method handles nonmonotone, noncoercive viscosity terms effectively.
- Provides a framework for similar nonlinear evolution problems.

## Abstract

In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and {\it a priori} bounds that permit passing to the limit, we prove that the problem has a solution.