Existence theory for nonlinear Fredholm and Volterra integral equations on half-open intervals

In this chapter we present existence theory for the nonlinear Fredholm integral equation $$ y(t) = h(t) + \smallint _0^T k(t,s)g(s,y(s))ds,$$ (4.1.1) and the nonlinear Volterra integral equation $$ y(t) = h(t) + \smallint _0^t k(t,s)g(s,y(s))ds,$$ (4.1.2) when both are defined on the compact interval [0, T]. Naturally we first concern ourselves with existence principles for both equations.

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