Periodic Solutions of a Class of Hyperbolic Equations Containing a Small Parameter

摘要

A method is discussed to determine the solutions u(t,x) and v(y,z) of the problems (u sub tt - u sub xx) = epsilon g(t,x,u, u sub t, u sub x), u(t, 0) = u(t, pi) = 0, and v sub yz = epsilon f (y,z,v, v sub y, v sub z), respectively, with u(t + 2 pi, x) = u(t,x), v(y + 2 pi, z) = v(y,z) = v(y,z + 2 pi) provided that g is 2 pi -periodic in t and f is 2 pi- periodic in y, z, and epsilon is a small real parameter.