Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

In-Sook Kim ; Jung-Hyun Bae

Open Mathematics, Tome 11 (2013), p. 851-864 / Harvested from The Polish Digital Mathematics Library

Résumé

Let X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: X⊃D(T) → 2X* is a maximal monotone multi-valued operator and C: X⊃D(C) → X* is a generalized pseudomonotone quasibounded operator with L ⊂ D(C), where L is a dense subspace of X. Applying a recent degree theory of Kartsatos and Skrypnik, we establish the existence of an eigensolution to the nonlinear inclusion 0 ∈ T x + λ C x, with a regularization method by means of the duality operator. Moreover, possible branches of eigensolutions to the above inclusion are discussed. Furthermore, we give a surjectivity result about the operator λT + C when λ is not an eigenvalue for the pair (T, C), T being single-valued and densely defined.

Détail

Publié le : 2013-01-01

Zbl 1320.47061

EUDML-ID : urn:eudml:doc:269385

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