International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 12, Pages 751-760
doi:10.1155/S0161171202109276

On the relation between interior critical points of positive solutions and parameters for a class of nonlinear boundary value problems

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 f∈c2[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.