On a nonlinear Schrödinger equation with indefinite potential

We investigate the semilinear Schrödinger equation −Δu+V(x)u=Q(x)f(u),inRN, where N≥3, V(x)∈LlocN/2(RN) and Q(x)∈L∞(RN), V(x) and Q(x) respectively tend to some positive limits V∞ and Q∞ as |x|→∞, and f∈C(R) is a superlinear and subcritical function. Assuming some weak one-sided asymptotic estimates for V(x) and Q(x), we prove that the above equation has a positive ground state solution and a least energy nodal solution via the minimization method constrained to Nehari type sets.