Green's function to the forced Duffing equation involving nonlocal integral conditions by Green's functional concept

Abstract

In this work, by Green's functional concept we propose a Green's function to a nonlinear problem for the forced Duffing equation involving linear nonlocal integral conditions. To this end, a system of three integro-algebraic equations called the special adjoint system is constructed. And a condition for existing the unique solution to this system is presented. The unique solution of this special adjoint system is Green's functional. In accordance with this condition, the special adjoint system is reduced to an integral equation yielding the first component of Green's functional. This component represents Green's function for that problem. In order to illustrate the theoretical presentation, an application is provided. © 2012 American Institute of Physics.