English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let X be a real reflexive Banach space with dual X* and G C X open and bounded and such that 0 ∈ G. Let T: X ⊃ D(T) → 2 X* be maximal monotone with 0 ∈ D(T) and 0 ∈ T(0), and C: X ⊃ D(C) → X* with 0 E D(C) and C(0) ≠ 0. A general and more unified eigenvalue theory is developed for the pair of operators (T, C). Further conditions are given for the existence of a pair (A, x) ∈ (0, ∞ ) x (D(T + C) n ∂G) such that (**) Tx+λCx? 0. The "implicit" eigenvalue problem, with C(λ, x) in place of λCx, is also considered. The existence of continuous branches of eigenvectors of infinite length is investigated, and a Fredholm alternative in the spirit of Necas is given for a pair of homogeneous operators T, C. No compactness assumptions have been made in most of the results. The degree theories of Browder and Skrypnik are used, as well as the degree theories of the authors involving densely defined perturbations of maximal monotone operators. Applications to nonlinear partial differential equations are included.

On the eigenvalue problem for perturbed nonlinear maximal monotone operators in reflexive Banach spaces