摘要
We study evolutionary bifurcation diagrams for the p-Laplacian generalized logistic problem (Equation presented), where p > 1, λ > 0 is a bifurcation parameter and µ ≥ 0 is the harvesting parameter. We assume that h, k satisfy h(0) = k(0) = 0, h(u), k(u) > 0 on (0, ∞), and h, k satisfy certain hypotheses such that, for each λ > 0, g <sub>λ</sub> (u):= h(u) - <sup>k</sup> (u) is positive and strictly p-concave on (0, ζ <sub>λ</sub> ), where ζ <sub>λ</sub> is the unique λ positive zero of g <sub>λ</sub> (u). We mainly prove that, for fixed µ > 0, on the (λ, kuk <sub>∞</sub> )plane, the bifurcation diagram always consists of a ⊂-shaped curve and then we study the structures and evolution of bifurcation diagrams for varying µ > 0. We give two interesting applications.