Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 755-767

NONLINEAR NONHOMOGENEOUS ROBIN PROBLEMS WITH CONVECTION

Pasquale Candito, Leszek Gasinski and Nikolaos S. Papageorgiou

University of Reggio Calabria, Department DICEAM
Via Graziella (Feo Di Vito), 89122 Reggio Calabria, Italy; pasquale.candito 'at' unirc.it

Pedagogical University of Cracow, Department of Mathematics
Podchorazych 2, 30-084 Cracow, Poland; leszek.gasinski 'at' up.krakow.pl

National Technical University, Department of Mathematics
Zografou Campus, Athens 15780, Greece; npapg 'at' math.ntua.gr

Abstract. We consider a Robin problem driven by a nonlinear, nonhomogeneous differential operator with a drift term (convection) and a Carathéodory perturbation. Assuming that the drift coefficient is positive and using a topological approach based on the Leray–Schauder alternative principle, we show that the problem has a positive smooth solution.

2010 Mathematics Subject Classification: Primary 35J60, 35J92.

Key words: Leray–Schauder alternative principle, nonlinear regularity, compact map, nonlinear maximum principle.

Reference to this article: P. Candito, L. Gasinski and N. S. Papageorgiou: Nonlinear nonhomogeneous Robin problems with convection. Ann. Acad. Sci. Fenn. Math. 44 (2019), 755-767.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4438