  We study how the properties of a Lagrangian density for a single real scalar
field in flat spacetime change with inclusion of an overall factor depending
only on the field. The focus of the paper is to obtain analytical results. So,
we show that even though it is possible to perform a field redefinition to get
an equivalent canonical model, it is not always feasible to write the canonical
model in terms of elementary functions. Also, we investigate the behavior of
the energy density and the linear stability of the solutions. Finally, we show
that one can find a class of models that present the same energy density and
the same stability potential.
