A quasilinear problem without the Ambrosetti–Rabinowitz-type condition

Source abstract

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 not 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.