Abstract: In this paper, taking the search of steady state solutions of one-dimension reactiondiffusion problems as the background, we study the existence and asymptotic estimates of solutions of the singularly perturbed Robin problem
a (x, ε)y"=f(x,y,y',ε),
a₀y(0,ε)-b₀y' (0 ε)=A₀, a₁y(1,ε) + b₁y' (1,ε)=A₁,where it is assumed that f_y'≡0 or f_y'≢0 and f_y' ≤ 0.