Nonlinear algebraic systems with discontinuous terms

TL;DR

This paper proves the existence of multiple solutions for nonlinear algebraic systems with discontinuous terms using critical point theory, with applications to various difference inclusion problems.

Contribution

It introduces a novel application of a multiple critical points theorem to discontinuous nonlinear algebraic systems, expanding solution existence results.

Findings

At least three solutions exist for the studied systems.

Applicable to tridiagonal, fourth-order, and partial difference inclusions.

Demonstrates the effectiveness of critical point methods in discontinuous contexts.

Abstract

Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a parametric discrete differential inclusion problem involving a real symmetric and positive definite matrix. Applications to tridiagonal, fourth-order and partial difference inclusions are presented.