The monotone method for periodic differential equations with the non well-ordered upper and lower solutions

In this paper, we consider the following periodic problem: x″(t)=g(t,x(t),x′(t)),a.e. t∈(a,b),x(a)=x(b),x′(a)=x′(b). The unique solution is obtained by constructing an auxiliary periodic system with bounded solutions and proving these bounds to be equal, in which case they are the expected unique solution.