Continuous dependence of boundary values for semiinfinite interval ordinary differential equations

Certain elliptic equations arising in catalysis theory can be transformed into ordinary differential equations on the interval(0,∞). The solutions to these problems usually depend on parametersρ∈ℝn, sayu(t,ρ). For certain types of nonlinearities, we show that the boundary valueu˙(∞,ρ)is continuous on compact sets of the variableρ. As a consequence, bifurcation results for the elliptic equation are obtained.