Bifurcation from the essential spectrum for some non‐compact non‐linearities
Charles A. Stuart, Klaus Kirchgässner · Mathematical Methods in the Applied Sciences · 1989
Abstract Conditions ensuring bifurcation from the infimum of the essential spectrum are given. The main result concerns non‐linear eigenvalue problems with variational structure in a Hilbert space. It extends previous results of a similar nature by admitting situations where the non‐linearity is not compact with respect to the graph norm of the linearization. The general result is applied to non‐linear elliptic equations on RN.