A complete classification of bifurcation diagrams of a \(p\)-Laplacian Dirichlet problem. II. Generalized nonlinearities (Q1936064)
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scientific article; zbMATH DE number 6137969
| Language | Label | Description | Also known as |
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| English | A complete classification of bifurcation diagrams of a \(p\)-Laplacian Dirichlet problem. II. Generalized nonlinearities |
scientific article; zbMATH DE number 6137969 |
Statements
A complete classification of bifurcation diagrams of a \(p\)-Laplacian Dirichlet problem. II. Generalized nonlinearities (English)
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21 February 2013
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The authors examine the bifurcation diagrams of classical positive solutions of the Dirichlet problem for the one-dimensional \(p\)-Laplace equation \[ -(\phi(u'))' = \lambda f(u), \] where \( \lambda \) is a positive parameter. They assume \(f(u) = |u-1|^q\) for \(0\leq u \leq 1\) and \(f(u) = |u-1|^r\) for \( u > 1\), with \(q,r>0\). The method is based on the study of the time-map. For part I, see [the second author and \textit{T.-S. Yeh}, Nonlinear Anal., Theory Methods Appl. 64, No. 11, A, 2412--2432 (2006; Zbl 1096.34014)].
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bifurcation diagram
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positive solution
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exact multiplicity
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\(p\)-Laplacian
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time map
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