On a class of periodic boundary value problems appearing in laser dynamics

We consider the periodic boundary value problem for the perturbed equation (Formula presented.) under the assumption that the unperturbed problem has a manifold of solutions. After suitable transformations, we apply the implicit function theorem to establish the existence of a family of solutions p(t, ε) to the periodic boundary value problem for sufficiently small ε. Furthermore, we present a schema to determine higher-order approximations of p(t, ε) in ε.