We consider the nonlinear boundary value problem
(
∗
)
L
u
+
λ
f
(
u
)
=
0
({\ast })Lu + \lambda f(u) = 0
,
x
∈
Ω
,
u
=
σ
ϕ
,
x
∈
∂
Ω
x \in \Omega ,\,u = \sigma \phi ,\,x \in \partial \Omega
, where
L
L
is a second order elliptic operator and
λ
\lambda
and
σ
\sigma
are parameters. We analyze global properties of solution continua of these problems as
λ
\lambda
and
σ
\sigma
vary. This is done by investigating particular sections, and special interest is devoted to questions of how solutions of the
σ
=
0
\sigma = 0
problem are embedded in the two-parameter family of solutions of
(
∗
)
({\ast })
. As a natural biproduct of these results we obtain (a) a new abstract method to analyze bifurcation from infinity, (b) an unfolding of the bifurcations from zero and from infinity, and (c) a new framework for the numerical computations, via numerical continuation techniques, of solutions by computing particular one-dimensional sections.