Abstract

We consider the boundary value problem u(x)=λf(u(x)), x(0,1); u(0)=0; u(1)+αu(1)=0, where α>0, λ>0 are parameters and fc2[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)=0sf(t)dt) the relation between λ and the number of interior critical points of the nonnegative solutions of the above system.