Abstract
We study the bifurcation diagrams of classical positive solutions u with {double pipe}u{double pipe} <sub>∞</sub> ∈ (0,∞) of the p-Laplacian Dirichlet problem where p > 1, φ <sub>p</sub> (y) = {pipe}y{pipe} <sup>p-2</sup> y, (φ <sub>p</sub> (u'))' is the one-dimensional p-Laplacian, λ > 0 is a bifurcation parameter, and with positive constants q and r. We give explicit formulas of bifurcation curves of classical positive solutions on the (λ, {double pipe}u{double pipe} <sub>∞</sub> )-plane. More importantly, for different (p, q, r), we give a complete classification of all bifurcation diagrams. Hence we are able to determine the (exact) multiplicity of classical positive solutions for each (p, q, r, λ). Our results generalize the results of Lee et al. [J. Math. Anal. Appl., 330 (2007), 276-290] with nonlinearity f <sub>q,r</sub> generalized from q = r > 0 to q, r > 0.