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A Brezis–Oswald approach for mixed local and nonlocal operators

    https://doi.org/10.1142/S0219199722500572Cited by:30 (Source: Crossref)

    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.

    p,s=Δp+(Δ)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.

    AMSC: 35A01, 35R11

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