Green's function for a differential equation with a deviating argument

A method for constructing the Green's function for a differential equation with a deviating argument is proposed, and the boundary-value problem
$$ x''(t)+p(t)\sigma(t)x(h(t))=f(t),\quad t\in[a,b],\quad x(a)=x(b)=0 $$
is used as an example. The method increases the possibilities for construction of Green's functions compared to the present methods, including the possibilities for representation of the Green's function in terms of the Cauchy function.