Periodic solutions of forced Kirchhoff equations

Abstract

We consider Kirchhoff equations for vibrating strings and elastic membranes under the action of an external forcing of period 2pi / omega and small amplitude epsilon. We prove existence, regularity and local uniqueness of 2pi / omega - periodic solutions of order epsilon by means of a Nash-Moser iteration scheme; the results hold for parameters (omega, epsilon) in a Cantor-like set which has asymptotically full measure for epsilon tends to 0.