Singular elliptic problem involving a Hardy potential and lower order term

Article type: Research Article

Authors: Sbai, Abdelaaziz^{; *} | El Hadfi, Youssef | El Ouardy, Mounim

Affiliations: Laboratory LIPIM, Sultan Moulay Slimane University, National School of Applied Sciences, Khouribga, Morocco

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider the following non-linear singular elliptic problem (1)−div(M(x)|∇u|p−2∇u)+b|u|r−2u=aup−1|x|p+fuγin Ωu>0in Ωu=0on ∂Ω, where 1<p<N; Ω⊂RN is a bounded regular domain containing the origin and 0<γ<1, a⩾0,b>0,0⩽f∈Lm(Ω) and 1<m<Np. The main goal of this work is to study the existence and regularizing effect of some lower order terms in Dirichlet problems despite the presence of Hardy the potentials and the singular term in the right hand side.

Keywords: Singular non-linearity, Hardy Potential, p-Laplacian, Lower Order Terms, Regularizing Effect

DOI: 10.3233/ASY-231832

Journal: Asymptotic Analysis, vol. 134, no. 1-2, pp. 213-225, 2023