International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 525-530
doi:10.1155/S0161171286000650

Continuous dependence of boundary value 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.