Generalized periodic solutions of quasilinear equations

Abstract

We study a boundary-value periodic problem for the quasilinear equationu _ff −u _xx =F[u,u _f u _x ],u(0,t) =u (π,t),u (x, t + π/q) =u(x, t), 0 ≤x ≤π,t ∈ ℝ,q ∈ ℕ. We establish conditions under which the theorem on the uniqueness of a smooth solution is true.