Abstract
We study the bifurcation diagrams of classical positive solutions u with {norm of matrix} u {norm of matrix} <sub>∞</sub> ∈ (0, ∞) of the p-Laplacian Dirichlet problem{((φ <sub>p</sub> (u <sup>′</sup> (x))) <sup>′</sup> + λ f <sub>q</sub> (u (x)) = 0, - 1 < x < 1,; u (- 1) = 0 = u (1),) where p > 1, φ <sub>p</sub> (y) = | y | <sup>p - 2</sup> y, (φ <sub>p</sub> (u <sup>′</sup> )) <sup>′</sup> is the one-dimensional p-Laplacian, λ > 0 is a bifurcation parameter, and f <sub>q</sub> (u) = | 1 - u | <sup>q</sup> is defined on [0, ∞) with q > 0. More precisely, for different (p, q), we give a complete classification of bifurcation diagrams of classical positive solutions on the (λ, {norm of matrix} u {norm of matrix} <sub>∞</sub> )-plane. Hence we are able to determine the exact multiplicity of classical positive solutions for each (p, q, λ). © 2006 Elsevier Inc. All rights reserved.