Periodic solutions of hyperbolic partial differential equations in a strip

have been studied by 0. Vejvoda [9], J. K. Hale [5] and P. H. Rabinowitz [8]. L. Cesari [4] and J. K. Hale [5] have also considered the question of existence of periodic solutions in the large for (1.3). The approach in [2], [31, [4] and [5] is based on the method used by these authors for similar problems in ordinary differential equations [6]. The approach and techniques used by Rabinowitz can be considered as an extension of the methods of the theory of elliptic boundary value problems to hyperbolic equations. The results presented in the present paper neither contain the results of the previous authors nor are they contained in their