We consider the boundary value problem − u ″ ( x ) = λ f ( u ( x ) ) , x ∈ ( 0 , 1 ) ; u ′ ( 0 ) = 0 ; u ′ ( 1 ) + α u ( 1 ) = 0 , where 0$"> α > 0 , 0$"> λ > 0 are parameters and f ∈ c 2 [ 0 , ∞ ) such that f ( 0 ) < 0 . In this paper, we study for the two cases ρ = 0 and ρ = θ ( ρ is the value of the solution at x = 0 and θ is such that F ( θ ) = 0 where F ( s ) = ∫ 0 s f ( t ) d t ) the relation between λ and the number of interior critical points of the nonnegative solutions of the above system.