  We study inhomogeneous nonlinear second-order differential equations in one
dimension. The inhomogeneities can be point sources or continuous source
distributions. We consider second order differential equations of type
$\phi''(x) + V(\phi(x)) = Q \, \delta(x) $, where $V(\phi)$ is a continuous,
differentiable, analytic function and $Q \,\delta (x)$ is a point source. In
particular we study cubic functions of the form $V(\phi(x)) = A\,\phi(x) +
B\,\phi^3(x)$. We show that Green functions can be determined for modifications
of such cubic equations, and that such Green's functions can be used to
determine the solutions for cases where the point source is replaced by a
continuous source distribution.
