On the evolution and qualitative behaviors of bifurcation curves for a boundary value problem Original Research Article

We study the evolution and qualitative behaviors of bifurcation curves of positive solutions for View the MathML source{−u″(x)=λ(u(1−sinu)+up),−10λ>0 is a bifurcation parameter and p≥1p≥1 is an evolution parameter. On the (λ,‖u‖∞)(λ,‖u‖∞)-plane, we prove that the bifurcation curve has exactly one turning point where the curve turns to the left for p>2p>2, it is a monotone curve for p=2p=2, it has at least two turning points for View the MathML source1