Note on elliptic equations on closed manifolds with singular nonlinearities

We consider a general elliptic equation $$-{\mathrm{\Delta }}_{g}u+V(x)u=f(x,u)+g(x,u^2)u$$ on a closed Riemannian manifold $(M,g)$ and utilize a recent variational approach by Hebey, Pacard, Pollack to show the existence of a nontrivial solution under general assumptions on nonlinear terms $f$ and $g$.