Periodic Solutions to the Wave Equation with Homogeneous Boundary Conditions

Abstract

We study time-periodic solutions to a quasilinear wave equation with homogeneous boundary conditions. We prove the existence of countably many periodic solutions in the case of boundary conditions of the third kind provided that the nonlinear term has power growth. It is shown that the Lp-norms of periodic solutions can be as large as desired. If the nonlinear term satisfies the nonresonance condition at infinity, we establish the existence of at least one periodic solution. We formulate a condition for the uniqueness of a periodic solution. Bibliography: 15 titles.