On ground states of superlinear p-Laplacian equations in

We consider superlinear p-Laplacian equations in R N with a potential which is periodic or has a bounded potential well. Without assuming the Ambrosetti–Rabinowitz type condition and the monotonicity of the function t ↦ f ( x , t ) | t | p − 1 , we prove the existence of ground states. Even for the case p = 2 , our results extend the recent results of Li, Wang and Zeng [Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006) 829–837].