Anti-periodic Solution for u y s u .. yu sf x, t.

Existence of a smooth anti-periodic solution for the quasilinear equation ut ty s ux..xyux x tsf x,t. inw0,px=R with the boundary condition u 0, t.su p , t.s0 is proved for a class of s ¨. including s ¨.s¨r ʹ1q¨ 2 , where f x, t. is a given anti-periodic function in t.