Representation of the Green's function for nonlinear differential equations

Marco Frasca, Asatur Khurshudyan

Published 2018-05-26Version 1

In this paper we study some classes of nonlinear second order ordinary differential equations allowing a specific representation for the Green's function. In particular, we show that if the nonlinear term possess a special multiplicative property, then its Green's function is represented as the product of the Heaviside function and the general solution of the Cauchy or boundary-value problem for the corresponding homogeneous equations. Hierarchies of specific equations admitting this representation are considered.