Fredholm Property of Nonlocal Problems for Integro-Differential Hyperbolic Systems

TL;DR

This paper investigates nonlocal boundary value problems for hyperbolic systems with integral conditions, demonstrating they are non-resonant and satisfy the Fredholm alternative under natural regularity assumptions.

Contribution

It establishes the Fredholm property and non-resonant behavior of nonlocal hyperbolic systems with integral boundary conditions, expanding understanding of their solvability.

Findings

Problems are non-resonant under regularity assumptions

Systems satisfy the Fredholm alternative

Results apply to continuous and time-periodic function spaces

Abstract

The paper concerns nonlocal time-periodic boundary value problems for first-order Volterra integro-differential hyperbolic systems with boundary inputs. The systems are subjected to integral boundary conditions. Under natural regularity assumptions on the data it is shown that the problems display completely non-resonant behaviour and satisfy the Fredholm alternative in the spaces of continuous and time-periodic functions.