Continuous dependence of boundary values for semiinfinite interval ordinary differential equations

Abstract

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 parameters ρ∈ℝn, say u(t,ρ). For certain types of nonlinearities, we show that the boundary value u˙(∞,ρ) is continuous on compact sets of the variable ρ. As a consequence, bifurcation results for the elliptic equation are obtained.