Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 739-753

EXISTENCE OF POSITIVE SOLUTIONS FOR NONLINEAR ROBIN PROBLEMS WITH GRADIENT DEPENDENCE

Nikolaos S. Papageorgiou and Chao Zhang

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

Harbin Institute of Technology, Department of Mathematics and Institute for Advanced
Study in Mathematics, Harbin 150001, P.R. China; czhangmath 'at' hit.edu.cn

Abstract. We consider a nonlinear Robin problem driven by the p-Laplace differential operator and with a reaction term which depends also on the gradient (convection). 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 35J92, 35P30.

Key words: Convection, Leray–Schauder alternative principle, minimal positive solution, nonlinear regularity, nonlinear maximum principle.

Reference to this article: N. S. Papageorgiou and C. Zhang: Existence of positive solutions for nonlinear Robin problems with gradient dependence. Ann. Acad. Sci. Fenn. Math. 44 (2019), 739-753.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4437