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
Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran
Received 10 September 2001
Copyright © 2002 G. A. Afrouzi and M. Khaleghy Moghaddam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.