Eigenvalue results for pseudomonotone perturbations of maximal monotone operators |
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Authors: | In-Sook Kim Jung-Hyun Bae |
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Institution: | 1211. Department of Mathematics, Sungkyunkwan University, Cheoncheon-dong 300, Natural Science Building A, Suwon, 440-746, Republic of Korea
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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) → 2 X * 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. |
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