Solvability of semilinear equations with compact perturbations of operators of monotone type

Guan, Zhengyuan

doi:10.1090/S0002-9939-1994-1174492-4

Solvability of semilinear equations with compact perturbations of operators of monotone type
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Proc. Amer. Math. Soc. 121 (1994), 93-102 Request permission

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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