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Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

100%

Kim I.-S., Bae J.-H.

Open Mathematics

2013

tom 11

nr 5

851-864

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.

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators

88%

Ioan Boţ R., Grad S.-M.

Open Mathematics

2011

tom 9

nr 1

162-172

In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation when 0 belongs to the range of S + T. Several special cases are discussed, some of them delivering interesting byproducts.

Ograniczanie wyników

2 Open Mathematics

1 Bae J.-H.

1 Grad S.-M.

1 Ioan Boţ R.

1 Kim I.-S.

1 2013

1 2011

Wyniki wyszukiwania

Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators