Solvability of a nonlinear third-order periodic boundary value problem

In this paper, we study the existence of solutions for a third-order periodic boundary value problem x‴(t)+bx″(t)+g(t,x(t))=e(t),t∈(0,2π),x(0)=x(2π),x′(0)=x′(2π),x″(0)=x″(2π). By using the Leray–Schauder continuation theorem, we obtain the existence result of solutions for the problem, and give an example to demonstrate the applications of our result.