A generalized Pohožaev identity and uniqueness of positive radial solutions of Δu+g(r)u+h(r)up=0Δu+g(r)u+h(r)up=0

We show a new generalized Pohožaev identity for Δu+g(r)u+h(r)up=0Δu+g(r)u+h(r)up=0, and we apply it to show the uniqueness of a positive radial solution of the equation in a ball, the entire space, an annulus, or an exterior domain under Dirichlet boundary condition.