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 ) + b x ″ ( t ) + g ( t , x ( t ) ) = e ( t ) , t ∈ ( 0 , 2 π ) , x ( 0 ) = x ( 2 π ) , x ′ ( 0 ) = x ′ ( 2 π ) , x ″ ( 0 ) = x ″ ( 2 π ) . 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.