A periodic boundary value problem with switchings under nonlinear perturbations

Abstract We investigate the existence of solutions weakly nonlinear periodic boundary value problems for systems ordinary differential equations with switchings and construction these solutions. consider critical case where equation generating constants a boundary-value problem does not turn into an identity. improve classification noncritical cases construct iterative algorithm finding in case. As examples application constructed scheme, we obtain approximations to mathematical model nonisothermal chemical reactions. To check accuracy proposed approximations, evaluate discrepancies original equation.