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Bifurcation from the essential spectrum for some non‐compact non‐linearities
Author(s) -
Stuart C. A.,
Kirchgässner K.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110408
Subject(s) - mathematics , essential spectrum , eigenvalues and eigenvectors , spectrum (functional analysis) , infimum and supremum , hilbert space , bifurcation , linearization , norm (philosophy) , mathematical analysis , uniform norm , pure mathematics , nonlinear system , quantum mechanics , political science , law , physics
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 R N .