Differential and Integral Equations

Smooth bifurcation for an obstacle problem

Jan Eisner, Milan Kučera, and Lutz Recke

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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 $h$.

Article information

Differential Integral Equations, Volume 18, Number 2 (2005), 121-140.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]
Secondary: 34C23: Bifurcation [See also 37Gxx] 35J25: Boundary value problems for second-order elliptic equations 49J40: Variational methods including variational inequalities [See also 47J20] 74G60: Bifurcation and buckling


Eisner, Jan; Kučera, Milan; Recke, Lutz. Smooth bifurcation for an obstacle problem. Differential Integral Equations 18 (2005), no. 2, 121--140. https://projecteuclid.org/euclid.die/1356060225

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