Existence of multiple positive periodic solutions for delay differential equation whose order is a multiple of 4

摘要

This article shows the existence of positive periodic solutions for retarded, advanced, neutral, and ordinary differential equations whose order is a multiple of 4. First, we find a positive Green’s function explicitly. Then assuming that the coefficient of the unknown in the linear part of the equation is bounded above and below by positive constants, we find one and then three solutions by applying the Krasnoselskii and Legget–William fixed point theorems.