Some conditions for the existence of 4-periodic solutions in non-homogeneous differential equations involving piecewise alternately advanced and retarded arguments

The manuscript introduces a method to characterize 4-periodic solutions in first-order non-homogeneous differential equations involving piecewise alternately advanced and retarded argument. It systematically delineates the prerequisites for these solutions to exist and furnishes precise methodologies for their determination. Additionally, the paper includes the illustrative example, including scenarios with infinitely many solutions, to demonstrate the effectiveness of the proposed approach.