Discontinuous functional differential equations with delayed or advanced arguments

TL;DR

This paper establishes new existence results for extremal solutions of discontinuous differential equations with delayed or advanced arguments, accommodating discontinuous boundary conditions that depend on the solution.

Contribution

It introduces novel theoretical results on extremal solutions for a class of discontinuous differential equations with deviated arguments and complex boundary conditions.

Findings

Existence of extremal solutions proven for specific discontinuous differential equations.

Boundary conditions can be discontinuous and depend functionally on the solution.

Applicable to equations with both delayed and advanced arguments.

Abstract

We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend functionally on the unknown solution.