A complete classification of bifurcation diagrams of a p ‐Laplacian Dirichlet problem

We study the bifurcation diagrams of (classical) positive solutions u with | u | ∞ ∈ (0, ∞) of the p ‐Laplacian Dirichlet problem ( φ p ( u ′( x )))′ + λf q ( u ( x ))) = 0, –1 ≤ x ≤ 1, u (–1) = 0 = u (1), where p > 1, φ p ( y ) = | y | p –2 y , ( φ p ( u ′))′ is the one‐dimensional p ‐Laplacian, λ > 0 is a bifurcation parameter, and the nonlinearity f q ( u ) = |1 – u | q is defined on [0, ∞) with constant q > 0. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)