Forced Oscillations of Systems Governed by One-Dimensional Non-Linear Wave Equations

Solutions of linear wave equations for forced oscillations in a finite region become infinite or large at and near resonant frequencies. For certain one-dimensional forced oscillation problems for the non-linear wave equations from which the linear ones are derived solutions appear to exist at all frequencies. A perturbation procedure for obtaining these solutions at and near the linear resonant frequencies and at other frequencies when the amplitudes of the oscillations are small is given.