Multiplicity of positive solutions for mixed local-nonlocal singular critical problems

We prove the existence of at least two positive weak solutions for mixed local-nonlocal singular and critical semilinear elliptic problems in the spirit of Hirano et al. (J Differ Equ 189(2):487–512, 2003), extending the recent results in Garain (J Geom Anal 33:212, 2023) concerning singular problems and, at the same time, the results in Biagi et al. (A Brezis–Nirenberg type result for mixed local and nonlocal operators, https://arxiv.org/abs/2209.07502, 2023) regarding critical problems.