A complete classification of bifurcation diagrams of a p -Laplacian Dirichlet problem |
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Authors: | Shin-Yi Lee Jong-Yi Liui Shin-Hwa Wang Chiou-Ping Yei |
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Institution: | Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan |
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Abstract: | We 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) |
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