Periodic Solutions of Nonlinear Integral Equations

The existence of a continuous periodic solution of the system x(t)=f(t)+t∫−∞q(t,s,x(s))ds, is studied using Horn\u27s fixed point theorem as the basic tool. First it is assumed that the solutions are bounded in some sense and that they depend continuously on initial functions. Then the required boundedness of solutions are obtained for special cases of q. Also, a few sufficient conditions are provided to ensure the continuous dependence of solutions on initial functions