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Proceedings of the American Mathematical Society

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



Existence theorems for generalized Hammerstein equations

Authors: P. N. Srikanth and M. C. Joshi
Journal: Proc. Amer. Math. Soc. 78 (1980), 369-374
MSC: Primary 45G10; Secondary 47H15
MathSciNet review: 553379
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Abstract: In this paper we obtain existence theorems for generalized Hammerstein-type equations $ K(u)Nu + u = 0$, where for each u in the dual $ {X^\ast}$ of a real reflexive Banach space $ X,K(u):X \to {X^\ast}$ is a bounded linear map and $ N:{X^\ast} \to X$ is any map (possibly nonlinear). The method we adopt is totally different from the methods adopted so far in solving these equations. Our results in the reflexive space generalize corresponding results of Petry and Schillings.

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