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.
Biagi S., Vecchi E. (2024). Multiplicity of positive solutions for mixed local-nonlocal singular critical problems. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 63(9), 1-45 [10.1007/s00526-024-02819-0].
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems
Vecchi E.
2024
Abstract
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.| File | Dimensione | Formato | |
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