  The Bethe-Salpeter (BS) equation in the ladder approximation is studied
within a scalar theory: two scalar fields (constituents) with mass $m$
interacting via an exchange of a scalar field (tieon) with mass $\mu$. The BS
equation is written in the form of an integral equation in the configuration
Euclidean $x$-space with the kernel which for stable bound states $M<2m$ is a
self-adjoint positive operator. The solution of the BS equation is formulated
as a variational problem. The nonrelativistic limit of the BS equation is
considered. The role of so-called abnormal states is discussed. The analytical
form of test functions for which the accuracy of calculations of bound state
masses is better than 1% (the comparison with available numerical calculations
is done) is determined. These test functions make it possible to calculate
analytically vertex functions describing the interaction of bound states with
constituents. As a by-product a simple solution of the Wick-Cutkosky model for
the case of massless bound states is demonstrated.
