We study the numerical solvability of a class of nonlinear weakly singular integral equations of Volterra-Hammerstein type with noncompact kernels. We obtain existence and uniqueness results and analyze the product integration methods for these equations under some verifiable conditions on the kernels and nonlinear functions. The convergence analysis is investigated and finally numerical experi...

in this paper‎, ‎existence of an $l^p$-solution for 2dies (two‎ ‎dimensional integral equations) of the hammerstein type is‎ ‎discussed‎. ‎the main tools in this discussion are schaefer's and‎ ‎schauder's fixed point theorems with a general version of‎ ‎gronwall's inequality‎.

We investigate local convergence of an SQP method for non-linear optimal control of weakly singular Hammerstein integral equations. Suucient conditions for local quadratic convergence of the method based are discussed.

Integral equations of mixed Voltera-Fredholm type arise in various physical and biological problems. In the present paper, we obtain the approximate solution of the nonlinear Volterra-Hammerstein integral equations of mixed type in terms of Taylor polynomial. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type x + KF (x) = 0 with the discontinuous semimonotone operator F . Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in Lp(Ω) are given for illustration.