Abstract
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 particular case, 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)).
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