  This paper is devoted to the study of the parameter's set where the Green's
function related to a general linear $n^{\rm th}$-order operator, depending on
a real parameter, $T_n[M]$, coupled with many different two point boundary
value conditions, is of constant sign. This constant sign is equivalent to the
strongly inverse positive (negative) character of the related operator on
suitable spaces related to the boundary conditions.
  This characterization is based on spectral theory, in fact the extremes of
the obtained interval are given by suitable eigenvalues of the differential
operator with different boundary conditions.
  Moreover, we also obtain a characterization of the strongly inverse positive
(negative) character on some sets, where non homogeneous boundary conditions
are considered.
  In order to see the applicability of the obtained results, some examples are
given along the paper. This method avoids the explicit calculation of the
related Green's function.
