Fixed Point Theory and Nonlinear Periodic Systems

Abstract

This work is concerned with a nonlinear periodic system, which depends on parameters. We investigate continuity with respect to parameters of the periodic solution of the system. Applying a fixed point theorem and the results regarding parameters for C₀- semigroups, we obtained some convenient conditions for determining both existence of a unique periodic solution and continuity in parameters of the periodic solution. The results are applied to a nonlinear wave equation with forced and damped boundary conditions.