On the Variational Method for the Existence of Solutions of Nonlinear Equations of Hammerstein Type

Djairo G. de Figueiredo and Chaitan P. Gupta
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Djairo G. de Figueiredo: University of Illinois, Department of Mathematics
Chaitan P. Gupta: University of Brasilia, Department of Mathematics

A chapter in Djairo G. de Figueiredo - Selected Papers, 1973, pp 35-41 from Springer

Abstract: ABSTRACT Let X be a real Banach space and X* its conjugate Banach space. Let A be an unbounded monotone linear mapping from X to X* and N a potential mapping from X* to X. In this paper we establish the existence of a solution of the equation u + ANu = v for a given v in X* using variational method. Our method consists in using a splitting of A via an auxiliary Hilbert space and solving an equivalent equation in this auxiliary Hilbert space. In §2, we prove the same result in the case when X is a Hilbert space using the natural splitting of A in terms of its square root. We do this to compare and contrast the proofs in the two cases.

Keywords: AMS (MOS) subject classifications (1970). Primary 47H15; 49G99; 45G05; 45G99; Variational method; Integral equations of Hammerstein type; Weak *-gradient; Carleman kernels (search for similar items in EconPapers)
Date: 1973
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DOI: 10.1007/978-3-319-02856-9_5

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