Existence and Regularity of Solutions to Elastic Systems With Nonlocal Conditions

ABSTRACT This manuscript investigates the existence and regularity of solutions for a class of damped elastic systems governed by a nonlinear evolution equation in Banach spaces, where the system's dynamics are influenced by a state‐dependent nonlocal condition. This generalized nonlocal condition extends several previously explored types of nonlocal conditions from the existing literature. By applying Schauder fixed‐point theorem under some conditions for the nonlinear functions, we establish the existence and regularity of mild solutions for the considered equation. Furthermore, a specific example is provided to demonstrate the practical application of these abstract results.