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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Galerkin methods in the constructive solvability of nonlinear Hammerstein equations with applications to differential equations

Authors: P. M. Fitzpatrick and W. V. Petryshyn
Journal: Trans. Amer. Math. Soc. 238 (1978), 321-340
MSC: Primary 47H15; Secondary 45G99
MathSciNet review: 0513094
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Abstract: We consider the solution of abstract Hammerstein equations by means of a Galerkin approximating scheme. The convergence of the scheme is proven by first establishing an equivalent scheme in a Hilbert space and then proving a convergence result for firmly monotone operators in a Hilbert space. The general results are applied to the case when the involved linear mapping is angle-bounded, and also to the treatment of certain differential equations.

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Keywords: Integral equations, Hammerstein, Galerkin approximation, firmly monotone operator, differential equation
Article copyright: © Copyright 1978 American Mathematical Society