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A complete classification of bifurcation diagrams of a p ‐Laplacian Dirichlet problem
Author(s) -
Lee ShinYi,
Liui JongYi,
Wang ShinHwa,
Yei ChiouPing
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701122
Subject(s) - bifurcation , laplace operator , constant (computer programming) , mathematics , bifurcation diagram , dirichlet distribution , p laplacian , nonlinear system , combinatorics , physics , pure mathematics , mathematical analysis , mathematical physics , computer science , quantum mechanics , boundary value problem , programming language
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)