Motivated by the study of systems of higher-order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral equations, where the nonlinearities and the functionals involved depend on some derivatives. We improve and complement earlier results in the literature. We also provide some examples in order to illustrate the applicability of the theoretical results. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

中文翻译：

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任意阶相关的扰动Hammerstein积分方程组的正解

受具有泛函边界条件的高阶边值问题系统研究的启发，我们通过拓扑方法讨论了一类相当一般的扰动 Hammerstein 积分方程系统的可解性，其中所涉及的非线性和泛函取决于一些衍生品。我们改进和补充了文献中的早期结果。我们还提供了一些例子来说明理论结果的适用性。本文是主题问题“微分和差分方程中的拓扑度和不动点理论”的一部分。