Classification of bifurcation curves of positive solutions for a nonpositone problem with a quartic polynomial

Abstract

We study exact multiplicity and bifurcation curves of positive solutions of the boundary value problemwhere σ, τ ∈ R, ρ ≥ 0, and λ > 0 is a bifurcation parameter. Then on the (λ, ||u||∞)-plane, we give a classification of four qualitatively different bifurcation curves: an S-shaped curve, a broken S-shaped curve, a ⊂-shaped curve and a monotone increasing curve.2000 Mathematics Subject Classification. Primary: 34B15, 34B18.