Existence and multiplicity of periodic solutions for a class of second-order ordinary differential equations

In this paper, we study the existence of positive periodic solutions for a class of non-autonomous second-order ordinary differential equations x ′ ′ + α x ′ + a ( t ) x n - b ( t ) x n + 1 + c ( t ) x n + 2 = 0 , where α ∈ R is a constant, n is a finite positive integer, and a ( t ), b ( t ), c ( t ) are continuous periodic functions. By using Mawhin’s continuation theorem, we prove the existence and multiplicity of positive periodic solutions for these equations.