On a smooth solution of a nonlinear periodic boundary-value problem

Abstract

We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu _tt - u_xx = ƒ(x, t, u, u, u _x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution.