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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On nonlinear equations of Hammerstein type in Banach spaces


Author: Peter Hess
Journal: Proc. Amer. Math. Soc. 30 (1971), 308-312
MSC: Primary 47.80
DOI: https://doi.org/10.1090/S0002-9939-1971-0282268-X
MathSciNet review: 0282268
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Abstract: A new theorem on the existence and uniqueness of a solution of an equation of Hammerstein type $ u + TNu = f$ is given. Here N denotes a (nonlinear) monotone mapping of a real reflexive Banach space X into its conjugate space $ {X^ \ast }$ and T a bounded monotone linear operator of $ {X^ \ast }$ into X. It is not assumed that T or N is coercive.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0282268-X
Keywords: Nonlinear Hammerstein equation, real reflexive Banach space, existence of solution, uniqueness of solution, maximal monotone mapping, angle-bounded linear operator
Article copyright: © Copyright 1971 American Mathematical Society