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On the relation between interior critical points and parameters for a class of nonlinear problems with Neumann–Robin boundary conditions

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  • Afrouzi, G.A.
  • Khaleghy Moghaddam, M.

Abstract

We consider 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 cases p∈(0,β) and p∈(β,θ) (p is the value of the solution at x=0 and β, θ are such that f(β)=0, F(θ)=∫0θf(t)dt=0), the relation between λ and the number of interior critical points of the positive solutions of the above system.

Suggested Citation

  • Afrouzi, G.A. & Khaleghy Moghaddam, M., 2006. "On the relation between interior critical points and parameters for a class of nonlinear problems with Neumann–Robin boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1109-1114.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:5:p:1109-1114
    DOI: 10.1016/j.chaos.2005.08.164
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    2. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    3. G. A. Afrouzi & M. Khaleghy Moghaddam, 2002. "On the relation between interior critical points of positive solutions and parameters for a class of nonlinear boundary value problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 31, pages 1-10, January.
    4. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
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