EXISTENCE OF POSITIVE SOLUTIONS FOR DAMPING ELASTIC SYSTEMS IN BANACH SPACES

The goal of this paper is to deal with the damped elastic systems with delay and nonlocal conditions in the framework of ordered Banach spaces. By combining a fixed point theorem for convex-power condensing operators with measures of noncompactness, we establish the existence of positive mild solutions for the aforementioned system. Our analysis assumes that the nonlinear function satisfies both measure conditions and order conditions. To demonstrate the practical applicability of our theoretical findings, we present a concrete example involving the vibration equation of a simply supported beam.