Periodic Solutions of a Class of Weakly Nonlinear Hyperbolic Partial Differential Equations

Abstract

In a recent paper A. C. Lazer gave a technique for the determination of periodic solutions of weakly nonlinear ordinary differential equations of the form ${{dx} / {dt}} = \varepsilon f(t,x,\varepsilon )$, where x and f are real k-vectors and $\varepsilon $ is a real parameter. In the present paper a method similar to that of Lazer is developed for the determination of periodic solutions of the weakly nonlinear hyperbolic system of the form $u_{xy} = \varepsilon f(x,y,u,u_x ,u_y ,\varepsilon )$. Both problems of obtaining periodic solutions in a strip and in the large are considered.