Bifurcation from the essential spectrum for some non‐compact non‐linearities | Zendy

Stuart C. A. | Zendy; Kirchgässner K. | Zendy

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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

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 .

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