Best constant and Mountain-Pass solutions for a supercritical Hardy-Sobolev problem in the presence of symmetries
نویسندگان
چکیده
Given a Riemannian manifold (M,g) and group G of isometries (M,g), we investigate the existence G-invariant positive solutions u:M→R to nonlinear equation Δgu+au=u2⋆(k,s)−1dg(x,Gx0)s+huq−1 where Δg=−divg(∇). The singularity nonlinearity are such that problem is critical for Hardy-Sobolev embeddings. We prove by using Aubin minimization Mountain-Pass lemma Ambrosetti-Rabinowitz. As product our analysis, find value best-constant in associated inequality.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2023
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2023.127437