Global Existence of Periodic Travelling Waves of an Infinite Non-Linearly Supported Beam

The paper deals with problems of existence of periodic travelling wave solutions with non-small amplitudes of a PDE describing oscillations of an infinite beam, which lies on a non-linearly elastic support. Such solutions are in fact critical points of a functional on a suitable functional space. By means of a minimax variational technique, the authors found a domain in the parameter space for which there exist periodic travelling waves of a certain fixed period $\Sigma$.