Nonlinear Hammerstein equations and functions of bounded Riesz-Medvedev variation
The authors consider the solvability of the Hammerstein integral equation \[ f(s)=\int_a^bk(s,t)h(t,f(t))\,dt+b(s). \] The main novelty of the paper seems to be the allowance of very weak regularity assumptions on the constituent functions in the integral equation and, in particular, the search for solutions of the equation within spaces of generalized bounded variation. While it is unfortunate that no concrete examples are provided to illustrate the abstract theory, the paper is relatively clearly written, and it should be of interest to researchers whose interests intersect existence theory for integral equations.
scientific article; zbMATH DE number 6700541