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

Fitzpatrick, P. M.; Petryshyn, W. V.

doi:10.1090/S0002-9947-1978-0513094-2

Galerkin methods in the constructive solvability of nonlinear Hammerstein equations with applications to differential equations
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by P. M. Fitzpatrick and W. V. Petryshyn PDF

Trans. Amer. Math. Soc. 238 (1978), 321-340 Request permission

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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Variational methods in the study of nonlinear operators