## Differential and Integral Equations

### Smooth bifurcation for an obstacle problem

#### Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012