Positivity results to iterative system of higher order boundary value problems

The present research explores the existence of positive solutions for the iterative system of higher-order differential equations with integral boundary conditions that include a non-homogeneous term. To address the boundary value problem, the solution is expressed as a solution of an equivalent integral equation involving kernels. Subsequently, bounds for these kernels are determined to facilitate further analysis. The primary tool employed in this study is the Guo-Krasnosel’skii fixed-point theorem, which is utilized to establish the existence of positive solutions within a cone of a Banach space. This approach enables a rigorous exploration of the existence of at least one positive solution and provides insights into the behavior of the differential equation under the given boundary conditions.