Existence of solutions for a nonlinear elliptic problem on a Riemannian manifold

Let (M,g)(M,g) be a noncompact, connected, orientable smooth N-dimensional Riemannian manifold without boundary. We consider the existence of solutions of problemequation(P)Δgu+aulogu=0on M, where ΔgΔg stands for the Laplacian in M   and a>0a>0.