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

Abstract

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