Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

In-Sook Kim; Jung-Hyun Bae

Open Mathematics (2013)

  • Volume: 11, Issue: 5, page 851-864
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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In-Sook Kim, and Jung-Hyun Bae. "Eigenvalue results for pseudomonotone perturbations of maximal monotone operators." Open Mathematics 11.5 (2013): 851-864. <http://eudml.org/doc/269385>.

@article{In2013,
abstract = {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.},
author = {In-Sook Kim, Jung-Hyun Bae},
journal = {Open Mathematics},
keywords = {Eigenvalues; Maximal monotone operators; Pseudomonotone operators; Degree theory; nonlinear inclusions; eigenvalues; maximal monotone operators; pseudomonotone operators; degree theory},
language = {eng},
number = {5},
pages = {851-864},
title = {Eigenvalue results for pseudomonotone perturbations of maximal monotone operators},
url = {http://eudml.org/doc/269385},
volume = {11},
year = {2013},
}

TY - JOUR
AU - In-Sook Kim
AU - Jung-Hyun Bae
TI - Eigenvalue results for pseudomonotone perturbations of maximal monotone operators
JO - Open Mathematics
PY - 2013
VL - 11
IS - 5
SP - 851
EP - 864
AB - 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.
LA - eng
KW - Eigenvalues; Maximal monotone operators; Pseudomonotone operators; Degree theory; nonlinear inclusions; eigenvalues; maximal monotone operators; pseudomonotone operators; degree theory
UR - http://eudml.org/doc/269385
ER -

References

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