Existence of solutions to fractional equations with Hardy potential on compact Riemannian manifolds

In this article, we study a fractional Laplace equation on a compact Riemannian manifold involving a Hardy potential and a nonlinearity with critical exponent, (-Δg)ˢ u - μ udg(x, x₀)²ˢ = λ f(x)|u|ᵖ⁻²u + k(x) |u|2ₛ^*-2u in M, where \( n > 2s \), \( s ∈ (0,1) \), \( 2 < p < 2_s^* \), and \( 2_s^* = 2n/n-2s \) denotes the fractional Sobolev critical exponent. Under suitable conditions on the parameters μ, λ and the smooth positive functions \( f \) and \( k \), we employ critical point theory to establish the existence of nontrivial solutions. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/38/abstr.html