In this paper, we consider the necessary and sufficient conditions of blow-up property of solutions to cordial Volterra integral equations (CVIEs). Following the framework in Brunner and Yang (J Integral Equations Appl 3:806–830, 2012), the necessary and sufficient conditions for the blow-up behavior of increasing solutions is investigated. Finally, the results are extended to fluctuating solutions with a reversal comparison theorem.

中文翻译：

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CVIE解决方案的爆炸行为分析

在本文中，我们考虑了亲和的Volterra积分方程（CVIE）解的爆破性质的充要条件。遵循Brunner和Yang的框架（J积分方程Appl 3：806–830，2012年），研究了增加解的爆炸行为的充要条件。最后，利用逆比较定理将结果扩展到波动解。