A Brezis–Oswald approach for mixed local and nonlocal operators
Stefano Biagi, Dimitri Mugnai, Eugenio Vecchi
Abstract
In this paper, we provide necessary and sufficient conditions for the existence of a unique positive weak solution for some sublinear Dirichlet problems driven by the sum of a quasilinear local and a nonlocal operator, i.e. [Formula: see text] Our main result is resemblant to the celebrated work by Brezis–Oswald [Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986) 55–64]. In addition, we prove a regularity result of independent interest.
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