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Mat. Zametki, 2002, Volume 71, Issue 2, Pages 214–226 (Mi mz340)  

Increasing Monotone Operators in Banach Space

G. I. Laptev

Tula State University

Abstract: An operator $A$ mapping a separable reflexive Banach space $X$ into the dual space $X'$ is called increasing if $\|Au\|\to \infty$ as $\|u\|\to \infty$. Necessary and sufficient conditions for the superposition operators to be increasing are obtained. The relationship between the increasing and coercive properties of monotone partial differential operators is studied. Additional conditions are imposed that imply the existence of a solution for the equation $Au=f$ with an increasing operator $A$.

DOI: https://doi.org/10.4213/mzm340

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English version:
Mathematical Notes, 2002, 71:2, 194–205

Bibliographic databases:

UDC: 517.9
Received: 23.03.2001

Citation: G. I. Laptev, “Increasing Monotone Operators in Banach Space”, Mat. Zametki, 71:2 (2002), 214–226; Math. Notes, 71:2 (2002), 194–205

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