Existence of solutions for semilinear elliptic equations with indefinite linear part

We study equations on RN, Lu = W(x)u p −1 uLu = f(u), where L is an indefinite Schrödinger operator, 0 ⩽ W(x) → 0 as× → ∞, and subcritical nonlinearities. We prove existence of solutions uϵH1(RN) via an inversion to a “dual” variational problem.