Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators |
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Authors: | Z Guan IV Skrypnik |
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Institution: | a Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire, WI 54702, USA b Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA c Institute for Applied Mathematics and Mechanics, R. Luxemburg Str. 74, Donetsk 340114, Ukraine |
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Abstract: | Let X be a real reflexive Banach space and be maximal monotone. Let be quasibounded, finitely continuous and generalized pseudomonotone with X′⊂D(B), where X′ is a dense subspace of X such that X′∩D(A)≠∅. Let S⊂X∗. Conditions are given under which and intS⊂intR(A+B). Results of Browder concerning everywhere defined continuous and bounded operators B are improved. Extensions of this theory are also given using the degree theory of the last two authors concerning densely defined perturbations of nonlinear maximal monotone operators which satisfy a generalized (S+)-condition. Applications of this extended theory are given involving nonlinear parabolic problems on cylindrical domains. |
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Keywords: | primary 47H14 47H07 47H11 |
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