Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

We analyse 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 give conditions for such existence and uniqueness in some cases. Finally, we illustrate these methods with an example of a collocation problem and give some examples of collocation problems that do not fit in the cases studied previously.