A quasilinear problem without the Ambrosetti–Rabinowitz-type condition

Leonelo Iturriaga; Sebastián Lorca; Pedro Ubilla

doi:10.1017/S0308210509000432

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.

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A quasilinear problem without the Ambrosetti–Rabinowitz-type condition

Abstract

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A quasilinear problem without the Ambrosetti–Rabinowitz-type condition

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