Seminar Analysis: Przemek Zieliński (Institute of Mathematics Polish Academy of Sciences)

Spectral methods in the study of semi-linear equations in Hilbert spaces.

I will present the results on the existence of solutions to semi-linear equation

    Lx+N(x)=0,

where L is a linear and N a nonlinear operator defined on Hilbert space. I concentrate on the case when 0 is in an essential spectrum of L. The two main methods which I use are: topological degree in infinite-dimensional spaces and the spectral theory for linear operators in Hilbert spaces. This results are part of my Ph.D. project. 

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