Constant-Sign Green’s Function of a Second-Order Perturbed Periodic Problem

Abstract

In this paper, we were interested in obtaining the exact expression and studying the regions of constant sign of Green’s function related to a second-order perturbed periodic problem coupled with integral boundary conditions at the extremes of the interval of the definition. To obtain the expression of Green’s function related to this problem, we used the theory presented in a previous paper of the authors for general non-local perturbed boundary-value problems. Moreover, we characterized the parameter set where such a Green’s function has a constant sign. To this end, we needed to consider first a related second-order problem without integral boundary conditions, obtaining the properties of its Green’s function and then using them to compute the sign of the one related to the main problem.

Keywords

• Green’s function
• periodic boundary-value problem
• integral boundary conditions