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, (-g) ˢ u - udg (x, x₀) ^{2s} = f (x) |u|^p-2u + k (x) |u|^2ₛ^*-2u in M, where \ (n > 2s \), \ (s (0, 1) \), \ (2 < p < 2ₛ^* \), and \ (2ₛ^* = 2nn-2s \) denotes the fractional Sobolev critical exponent. Under suitable conditions on the parameters, 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