We are concerning with a nonlinear Hammerstein quadratic integral equation. We prove the existence of at least one positive solution x ∈ L1 under Carathèodory condition. Secondly we will make a link between Peano condition and Carathèodory condition to prove the existence of at least one positive continuous solution. Finally the existence of the maximal and minimal solutions will be proved.

We present regularization methods for solving ill-posed Hammerstein type operator equations under weaker conditions than in earlier studies such as [13]. Our semilocal convergence analysis is based on majorizing sequences. Numerical examples where the new convergence criteria are satisfied but the old criteria are not satified are also presented at the end of the study. AMS (MOS) Subject Classi...

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

The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

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 is that we can applied for those integral equations whic...

Making use of the Volterra approach, black box modeling is applied to a large scale analog circuitry for an ADSL (asymmetric digital subscriber line) central office application. Reducing the number of free parameters through special assumptions on the Volterra kernels, one ends up with the Hammerstein model. Taking the first few taps of the Volterra kernels and approximating the last taps throu...

Most of the methods, which used to solve nonlinear integral equations, transform the equation into a system of nonlinear equations. It is cumbersome to solve these systems, or the solution may be unreliable. In this paper, we propose an iterative approach based on fixed point method and Sinc quadrature, which has exponentially rate of convergence, to solve Hammerstein integral equation. Converg...