Galerkin Methods in the Constructive Solvability of Nonlinear Hammerstein Equations with Applications to Differential Equations

P. M. Fitzpatrick, W. V. Petryshyn
1978 Transactions of the American Mathematical Society  
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 Hubert 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.
doi:10.2307/1997811 fatcat:lnpacrgmqfekvndldntzjaaamm