In this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in Banach spaces admitting the existence of a lower solution.

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...

This paper introduces a numerical method to solve anti-periodic boundary value problems. The proposed method converts anti-periodic boundary value problem to a Fredholm integral equation and solves it by Galerkin method. The approximate solution converges to the exact solution and satisfies anti-periodic boundary conditions completely. Also, the convergence rate of the proposed method is given ...

The initialand boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behavior (termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. To this aim, we derive a new formula representing solutions of this initialand boundary-value problem by inverting the operat...