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Nonlocal Lazer–McKenna-type problem perturbed by the Hardy’s potential and its parabolic equivalence
, Article Boundary Value Problems ; Volume 2021, Issue 1 , 2021 ; 16872762 (ISSN) ; Hesaaraki, M ; Karim Hamdani, M ; Thanh Chung, N ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2021
Abstract
In this paper, we study the effect of Hardy potential on the existence or nonexistence of solutions to the following fractional problem involving a singular nonlinearity: {(−Δ)su=λu|x|2s+μuγ+fin Ω,u>0in Ω,u=0in (RN∖Ω). Here 0 < s< 1 , λ> 0 , γ> 0 , and Ω ⊂ RN (N> 2 s) is a bounded smooth domain such that 0 ∈ Ω. Moreover, 0 ≤ μ, f∈ L1(Ω). For 0 < λ≤ Λ N,s, Λ N,s being the best constant in the fractional Hardy inequality, we find a necessary and sufficient condition for the existence of a positive weak solution to the problem with respect to the data μ and f. Also, for a regular datum of f, under suitable assumptions, we obtain some existence and uniqueness results and calculate the rate of...