Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth

Abstract

In this work we study an existence and multiplicity result for the following prescribed mean-curvature problem with critical growthwhere Ω is a bounded smooth domain of R N , N ≥ 3 and 1 < q < 2. In order to employ variational arguments, we consider an auxiliary problem which is proved to have infinitely many solutions by genus theory. A clever estimate in the gradient of the solutions of the modified problem is necessary to recover solutions of the original one.