Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

被引:1
|
作者
Kim, In-Sook [1 ]
Bae, Jung-Hyun [1 ]
机构
[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea
来源
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2013年 / 11卷 / 05期
基金
新加坡国家研究基金会;
关键词
Eigenvalues; Maximal monotone operators; Pseudomonotone operators; Degree theory; REFLEXIVE BANACH-SPACES;
D O I
10.2478/s11533-013-0211-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: XaS integral D(T) -> 2 (X) * is a maximal monotone multi-valued operator and C: XaS integral D(C) -> X* is a generalized pseudomonotone quasibounded operator with L aS, 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 a T (x) + lambda 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 lambda T + C when lambda is not an eigenvalue for the pair (T, C), T being single-valued and densely defined.
引用
收藏
页码:851 / 864
页数:14
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