# On the variational characterization of the Fucik Spectrum

Kdy? 24.10.2011 14:00 - 15:30 ZČU / FAV / KMA / UL610 (učebna)

## Stev Robinson: On the variational characterization of the Fucik Spectrum

Stručný abstrakt:

It is well known that the eigenvalues of a symmetric matrix, and more generally of a self-adjoint differential operator such as the Laplacian ($\Delta u=\nabla\cdot (\nabla u)$) can be characterized through a  minimax procedure involving the Rayleigh Quotient. An important question for nonlinear analysts to answer is "How can this idea be applied to nonlinear eigenvalue problems?" For example, what if the standard linear restoring force in a spring equation ($u''+\lambda u=0$) is replaced by an asymmetric restoring force of the sort found in suspension bridge models ($u''+\alpha u^+ - \beta u^-=0$). How can we understand the Fucik eigenpairs $(\alpha,\beta)$ using minimax ideas? In this talk I will discuss several variational approaches to this problem as well as some recent results do to this author and P. Drabek.