On solvability of one class of Hammerstein nonlinear integral equations

The article deals with one class of Hammerstein nonlinear integral equations with kernel depending on the sum and the difference of arguments. In the particular case of basic nonlinear equation the existence of one parameter family of solutions is proved. Using special solution of this family the solution of basic nonlinear equation is constructed and asymptotic behavior at infinity is investigated. At the end of the work some of examples are given.