Positive solutions for nonvariational Robin problems

Article type: Research Article

Authors: Papageorgiou, Nikolaos S.^a | Rădulescu, Vicenţiu D.^{b; *} | Repovš, Dušan D.^c

Affiliations: [a] Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece | [b] Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland & Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania | [c] Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia

Correspondence: [*] Corresponding author. E-mail: vicentiu.radulescu@imar.ro.

Abstract: We study a nonlinear Robin problem driven by the p-Laplacian and with a reaction term depending on the gradient (convection term). Using the theory of nonlinear operators of monotone-type and the asymptotic analysis of a suitable perturbation of the original equation, we show the existence of a positive smooth solution.

Keywords: Gradient dependence, pseudomonotone operator, nonlinear regularity, positive solution, nonlinear Picone’s identity

DOI: 10.3233/ASY-181464

Journal: Asymptotic Analysis, vol. 108, no. 4, pp. 243-255, 2018