Existence theorems for generalized Hammerstein equations

Srikanth, P. N.; Joshi, M. C.

doi:10.1090/S0002-9939-1980-0553379-1

Existence theorems for generalized Hammerstein equations
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by P. N. Srikanth and M. C. Joshi PDF

Proc. Amer. Math. Soc. 78 (1980), 369-374 Request permission

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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Verallgemeinerte Hammersteinsche Gleichungen und einige Anwendungen

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Existence theorems for operator equations of generalized Hammerstein type and some applications

On locally uniformly convex and differentiable norms in certain nonseparable Banach spaces

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