We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples ...

In this paper we prove the existence and the uniqueness of the solutions of the Hammerstein-Volterra integral equation in the space of the absolutely continuous functions endowed with the bounded variation norm. After that, we find the resolvent of the corresponding linear integral equation in order to obtain a variation of parameters formula for the solutions of this linear equation. Finally, ...

Abstract We consider a generic type of nonlinear Hammerstein-type integral equations with the particularity having non-differentiable kernel Nemystkii type. So, in order to solve it we uniparametric family iterative processes derivative free, main advantage that for special value involved parameter method obtained coincides Newton’s method, is due fact evaluating divided difference operator whe...