@Article{Filippucci2019,
author = "Filippucci, Roberta and Lini, Chiara",
title = "Existence results and a priori estimates for solutions of quasilinear problems with gradient terms",
journal = "Opuscula Math.",
year = "2019",
volume = "39",
number = "2",
pages = "195--206",
doi = "https://doi.org/10.7494/OpMath.2019.39.2.195",
url = "https://doi.org/10.7494/OpMath.2019.39.2.195",
abstract = "In this paper we establish a priori estimates and then an existence theorem of positive solutions for a Dirichlet problem on a bounded smooth domain in \(\mathbb{R}^N\) with a nonlinearity involving gradient terms. The existence result is proved with no use of a Liouville theorem for the limit problem obtained via the usual blow up method, in particular we refer to the modified version by Ruiz. In particular our existence theorem extends a result by Lorca and Ubilla in two directions, namely by considering a nonlinearity which includes in the gradient term a power of \(u\) and by removing the growth condition for the nonlinearity \(f\) at \(u=0\).",
keywords = "existence result, quasilinear problems, a priori estimates",
issn = "1232-9274"
}