What do you mean by "nonlinear eigenvalue problems"?

Abstract

A nonlinear eigenvalue problem is generally described by an equation of the form F(λ, x) = 0, where F(λ, 0) = 0 for all λ, and contains by definition two unknowns: the eigenvalue parameter λ and the "nontrivial" vector(s) x corresponding to it. The nonlinear dependence of F can be in either of them (and of course in both), and also the research in this area seems to follow two quite different directions. In this review paper, we try to collect some points of possible common interest for both fields.