Remarks on the existence and uniqueness of solutions of Volterra functional equations in \(L^ p\) spaces (Q1182517)

Let \(B\) be a Banach space, \(I\) some interval on \(\mathbb{R}^ n\) and \(F:L^ p_{loc}(I,B)\to L^ p_{loc}(I,B)\). The author studies equations of the form (+) \(x(t)=(Fx)(t)\) for \(t\in I\). The existence and uniqueness of a solution \(x^*\in L^ p_{loc}(I,B)\) of (+) and its iterative construction are proved under some general conditions. Special cases are considered.