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2005 Smooth bifurcation for an obstacle problem
Jan Eisner, Milan Kučera, Lutz Recke
Differential Integral Equations 18(2): 121-140 (2005). DOI: 10.57262/die/1356060225


The existence of smooth families of solutions bifurcating from the trivial solution for a two-parameter bifurcation problem for a class of variational inequalities is proved. As an example, a model of an elastic beam compressed by a force $\lambda$ and supported by a unilateral connected fixed obstacle at the height $h$ is studied. In the language of this example, we show that nontrivial solutions touching the obstacle on connected intervals bifurcate from the trivial solution and form smooth families parametrized by $\lambda$ and $h$. In particular, the corresponding contact intervals depend smoothly on $\lambda$ and $h$.


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Jan Eisner. Milan Kučera. Lutz Recke. "Smooth bifurcation for an obstacle problem." Differential Integral Equations 18 (2) 121 - 140, 2005.


Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1201.74125
MathSciNet: MR2106098
Digital Object Identifier: 10.57262/die/1356060225

Primary: 47J15
Secondary: 34C23 , 35J25 , 49J40 , 74G60

Rights: Copyright © 2005 Khayyam Publishing, Inc.


Vol.18 • No. 2 • 2005
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