  We consider an elliptic problem with nonlinear boundary condition involving
nonlinearity with superlinear and subcritical growth at infinity and a
bifurcation parameter as a factor. We use re-scaling method, degree theory and
continuation theorem to prove that there exists a connected branch of positive
solutions bifurcating from infinity when the parameter goes to zero. Moreover,
if the nonlinearity satisfies additional conditions near zero, we establish a
global bifurcation result, and discuss the number of positive solution(s) with
respect to the parameter using bifurcation theory and degree theory.
