Mass effect on an elliptic PDE involving two Hardy-Sobolev critical exponents

2023/09/09 by El Hadji Abdoulaye Thiam, Thiam, El Hadji Abdoulaye
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2309.04767

openalex publication_date 2023/09/09 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28

Abstract

We let Ω be a bounded domain of ℝ3 and Γ be a closed curve contained in Ω. We study existence of positive solutions u ∈ H10(Ω) to the equation -Δu+hu=λρ-s1Γu5-2s1+ρ-s2Γu5-2s2 \textrm in Ω where h is a continuous function and ρΓ is the distance function to Γ. We prove existence of solutions depending on the regular part of the Green function of linear operator. We prove the existence of positive mountain pass solutions for this Euler-Lagrange equation depending on the mass which is the regular part of the Green function of the linear operator -Δ+h.

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