Higher order Brezis-Nirenberg problem on hyperbolic spaces: Existence, nonexistence and symmetry of solutions

نویسندگان

چکیده

The main purpose of this paper is to establish the existence, nonexistence and symmetry nontrivial solutions higher order Brezis-Nirenberg problems associated with GJMS operators Pk on bounded domains in hyperbolic space Hn as well entire Hn. Among techniques different from problem Euclidean spaces, one our novelties study existence use crucially Helgason-Fourier analysis spaces Hardy-Sobolev-Maz'ya inequalities careful delicate properties Green's functions Pk−λ which are independent interests dealing such problems. Such allow us obtain integral representations thus avoid using maximum principle by developing a moving plane method form spirit work [14].

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ژورنال

عنوان ژورنال: Advances in Mathematics

سال: 2022

ISSN: ['1857-8365', '1857-8438']

DOI: https://doi.org/10.1016/j.aim.2022.108259