Abstract:The solvability of the equation $Au - Tu + Cu = f$ is studied under various assumptions of monotonicity and compactness on the operators A, T, and C, which map subsets of a reflexive Banach space X into its dual space. It is nowhere assumed that X possesses a Schauder basis or that the operator T is positive definite and selfadjoint. The results extend and/or improve recent results obtained by Chen, Kartsatos and Mabry, and Kesavan.
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- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 93-102
- MSC: Primary 47H15; Secondary 47H05, 47H11
- DOI: https://doi.org/10.1090/S0002-9939-1994-1174492-4
- MathSciNet review: 1174492