About Solutions in the Broad Sense of Nonlinear Systems

ABSTRACT Using the method of characteristics this work investigates the existence of periodic solutions in the broad sense for nonlinear systems with non‐uniform principal parts where the linear part does not decompose into independent homogeneous equations. Under the assumptions of continuity, boundedness and periodicity in some of the variables of the initial data, solutions in the broad sense are constructed. To study the solutions in the broad sense of a nonlinear system, nonlinear integral operators are constructed within a ball based on integral representations of solutions periodic in some variables for linear systems. The fixed‐point principle is then applied to these operators.