Based on the fixed point index theory for a Banach space, nontrivial periodic solutions are found for a class of integral equation of the form φ(x) = Z [x,x+ω]∩Ω K(x, y)f(y, φ(y − τ(y))) dy, x ∈ Ω, where Ω is a closed subset of RN with perioidc structure. Nonlinear Hammerstein integral equations of the form

Special classes of nonlinear systems applied in engineering are nonlinear systems with both block-oriented Hammerstein and Wiener structures, respectively [1, 3, 4, 7, 8, 14]. There are a lot of papers devoted to the different aspects of the parametric identification of Hammerstein and Wiener systems and much less on that of the Hammerstein–Wiener (H-W) systems with so-called hard nonlinearitie...

Using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of Hammerstein type . The mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). The procedure of this method is so fast and don't need high cpu and complicated programming. The advantages of this method are that we can applied for those integral equations whi...

In this paper, we prove the existence of a weak solution for Dirichlet boundary value problem related to certain p(x)-Laplacian, by using degree theory after turning into Hammerstein equation. The right hand side is possibly discontinuous function in second variable satisfying some non-standard growth conditions.