Existence of an anti-periodic solution for the quasilinear wave equation with viscosity

We prove the existence of a strong anti-periodic solution for the quasilinear wave equation with viscosity u(tt) - div{sigma(\del u\(2)) del u} - Delta u(t) = f(x, t) in Omega x R under the Dirichlet boundary condition u(t)\(partial derivative Omega) = 0, where Omega is a bounded domain in R(N) with the boundary partial derivative Omega and sigma(v(2)) is a function like 1/root + v(2). (C) 1996 Academic Press, Inc.