In this work, we present new existence results for a system of quadratic integral equations of Fredholm type on the whole space $${\mathbb {R}}^n$$. By using a technique based on a fixed point theorem expressed in terms of some measures of noncompactness, we generalize existence results obtained in both Aghajani and Haghighi (Novi Sad J Math 44.1:59–73, 2014) and Arab (Filomat 30(11):3063–3073, 2016) to Fredholm type systems, we relax some assumptions, and extend by the way the results given in Ilhan and Ozdemir (Electron J Differ Equ. 2016(271):15, 2016) for a class of systems of equations. The asymptotic behaviour of solutions is also described.

中文翻译：

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Fredholm 型二次积分方程组解的渐近行为

在这项工作中，我们在整个空间 $${\mathbb {R}}^n$$ 上提出了 Fredholm 型二次积分方程组的新存在结果。通过使用基于不动点定理的技术，用一些非紧凑性度量表示，我们概括了在 Aghajani 和 Haghighi (Novi Sad J Math 44.1:59–73, 2014) 和 Arab (Filomat 30(11) :3063–3073, 2016) 到 Fredholm 类型系统，我们放宽一些假设，并通过 Ilhan 和 Ozdemir (Electron J Differ Equ. 2016(271):15, 2016) 中给出的结果扩展到一类系统方程。还描述了解的渐近行为。