摘要
We study the global bifurcation and exact multiplicity of positive solutions for the positone multiparameter problem (Equation presented) where λ > 0 is a bifurcation parameter and ϵ > 0 is an evolution parameter. Under some suitable hypotheses on f <sub>ϵ</sub> (u), we prove that there exists ϵ > 0 such that, on the (λ, ||u||∞)-plane, the bifurcation curve is S-shaped for 0 < ϵ < ϵ and is monotone increasing for ϵ ≥ ϵ. We give an application for this problem with a class of polynomial nonlinearities fϵ(u) = - ϵu <sup>p</sup> +bu <sup>2</sup> +cu+d of degree p ≥ 3 and coefficients ϵ,b, d > 0, c ≥ 0. Our results generalize those in Hung and Wang.