## Existence theory for nonlinear Fredholm and Volterra integral equations on half-open intervals.(English)Zbl 0920.45006

The authors study the existence of solutions of Volterra integral equations of the form $y(t) = h(t) + \int_0^t k(t,s)g(s,y(s)) ds, \quad 0\leq t < T,$ where $$0\leq T \leq \infty$$ with particular emphasis on the case $$T=\infty$$. Some results on the corresponding Fredholm equation $$y(t) = h(t) + \int_0^T k(t,s)g(s,y(s)) ds$$ are also given. First the authors derive some existence principles based mainly on a nonlinear alternative of Leray-Schauder type but with complicated assumptions. These principles are then used to derive a number of existence and comparison results, including results on the asymptotic behavior of the solution, with easily verifiable assumptions. In many cases the assumptions on the kernel $$k$$ involve some form of ”log-convexity”. A large number of examples are given too.

### MSC:

 45G10 Other nonlinear integral equations 45M05 Asymptotics of solutions to integral equations
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### References:

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