This work is devoted to the study of singular strongly non-linear integro-differential equations of the type

where f is a Carathéodory function, \(\Phi \) is a strictly increasing homeomorphism, and k is a non-negative integrable function, which is allowed to vanish on a set of zero Lebesgue measure, such that \(1/k \in L^p_\textrm{loc}({\mathbb {R}}^{+}_0)\) for a certain \(p>1\). By considering a suitable set of assumptions, including a Nagumo–Wintner growth condition, we prove existence and non-existence results for boundary value problems associated with the non-linear integro-differential equation of our interest in the sub-critical regime on the real half line.

这项工作致力于研究以下类型的奇异强非线性积分微分方程

其中f是 Carathéodory 函数，\(\Phi \)是严格递增同胚，k是非负可积函数，允许在一组零勒贝格测度上消失，使得\(1/k \在 L^p_\textrm{loc}({\mathbb {R}}^{+}_0)\) 中对于某个\(p>1\)。通过考虑一组合适的假设，包括 Nagumo-Wintner 增长条件，我们证明了与我们感兴趣的实数次临界状态中的非线性积分微分方程相关的边值问题的存在和不存在结果。半线。