Fredholm property of nonlocal problems for integro-differential hyperbolic systems

Abstract

The paper concerns nonlocal time-periodic boundary value problems for first-order 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 behavior and satisfy the Fredholm alternative in the spaces of continuous and time-periodic functions.

Keywords

• first-order integro-differential hyperbolic systems
• integral boundary conditions
• time-periodic solutions
• fredholm alternative
• non-resonant behavior