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 ydiv s <=u<2.=u4yDu sf x,t. in V=R t t t under the Dirichlet boundary condition u t.<­Vs0, where V is a bounded domain in RN with the boundary ­V and s ¨2. is a function like 1r ʹ1q¨2.