Influence of the curvature in the existence of solutions for a two Hardy-Sobolev critical exponents

2023/09/09 by Thiam, El Hadji Abdoulaye, Diatta, Abdourahmane
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.04768

Abstract

For N≥ 4, we let Ω be a bounded domain of ℝN and Γ be a closed curve contained in Ω. We study existence of positive solutions u ∈ H10(Ω) to the equation -Δu+hu=λρ-s1Γu^2^*s1-1+ρ-s2Γu^2^*s2-1 \textrm in Ω where h is a continuous function and ρΓ is the distance function to Γ. We prove the existence of a mountain pass solution for this Euler-Lagrange equation depending on the local geometry of the curve and the potential h.

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