We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. We discuss the spectral properties associated to a weighted eigenvalue problem and present a global bound for subsolutions. The Neumann condition that we take into account comprises, as a particularcase, the one that has been recently introduced in (Rev. Mat. Iberoam. 33(2) (2017), 377–416). Also, the results that we present here find a natural application to a logistic equation motivated by biological problems that has been recently considered in (Dipierro, Proietti Lippi and Valdinoci (2021)).

中文翻译：

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具有 Neumann 条件的混合算子的线性理论

我们在这里考虑在合适的 Neumann 条件下的一种新型混合局部和非局部方程。我们讨论了与加权特征值问题相关的谱属性，并提出了子解的全局界限。我们考虑的诺依曼条件包括，作为一种特殊情况，最近在 (Rev. Mat. Iberoam. 33(2) (2017), 377–416) 中引入的条件。此外，我们在此展示的结果自然适用于最近在 (Dipierro、Proietti Lippi 和 Valdinoci (2021)) 中考虑的生物问题驱动的逻辑方程。