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. Lp,s = -Cp + (-C)ps. 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.
