Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth - Figueiredo, Giovany M.; Pimenta, Marcos T. O. [UNESP] (My University, 2015)
In this work we study an existence and multiplicity of solutions for the prescribed mean-curvature problem with critical growth, -div(Formula Presented), where Ω is a bounded smooth domain of RN, N ≥ 3 and 1 < q < 2. 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 problem.
Keywords: Critical exponent; Prescribed mean-curvature problem; Variational methods