  In this article we are interested for the numerical study of nonlinear
eigenvalue problems. We begin with a review of theoretical results obtained by
functional analysis methods, especially for the Schrodinger pencils. Some
recall are given for the pseudospectra. Then we present the numerical methods
and results obtained for eigenvalues computation with spectral methods and
finite difference discretization, in infinite or bounded domains. Comparison
with theoretical results is done. The main difficulty here is that we have to
compute eigenvalues of strongly non-self-adjoint operators which are very
unstable.
