Abstract We study the existence of a positive solution for a class of nonlinear Schrödinger equations aligned - u+V (x) u=f (u), u D^1, 2 (RN), \ N 3. aligned - Δ u + V (x) u = f (u), u ∈ D 1, 2 (R N), N ≥ 3. Here the potential V is symmetric under a group action G O (N) G ⊂ O (N) and decay to zero at infinity, and the nonlinearity f, under very mild hypotheses, is asymptotically linear or superlinear and subcritical at infinity, not satisfying any monotonicity condition.
Pina et al. (Fri,) studied this question.