Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations
For researchers in numerical analysis, this provides theoretical conditions for solving a class of integral equations, but the results are incremental and limited to specific cases.
The paper analyzes collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity, establishing conditions for existence and uniqueness of nontrivial collocation solutions, and illustrating with examples.
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 of collocation problems that do not fit in the cases studied previously.