A quasilinear problem without the Ambrosetti-Rabinowitz-type condition

We study the existence of a positive solution of a p-superlinear equation involving the p-Laplacian operator. The main difficulty here is that the nonlinearity considered does Hot necessarily verify the well-known Ambrosetti-Rabinowitz condition. As an application; by performing an adequate change of variables we obtain an existence result of a quasilinear equation depending on the gradient.