TY  - JOUR
ID  - Filippucci2019
LB  - Filippucci2019
AU  - Filippucci, Roberta
AU  - Lini, Chiara
TI  - Existence results and a priori estimates for solutions of quasilinear problems with gradient terms
ST  - Existence results and a priori estimates for solutions of quasilinear problems with gradient terms
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 2
SP  - 195
EP  - 206
DO  - https://doi.org/10.7494/OpMath.2019.39.2.195
UR  - https://doi.org/10.7494/OpMath.2019.39.2.195
AB  - 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 \(u=0\).
KW  - existence result
KW  - quasilinear problems
KW  - a priori estimates
SN  - 1232-9274
ER  -