# American Institute of Mathematical Sciences

April  2019, 12(2): 287-295. doi: 10.3934/dcdss.2019020

## Robin problems for the p-Laplacian with gradient dependence

 1 Dipartimento di Matematica, Università di Bari, Via E. Orabona 4, 70125 Bari, Italy 2 Dipartimento di Scienze Ecologiche e Biologiche (DEB), Università della Tuscia, Largo dell'Università, 01100 Viterbo, Italy 3 Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

* Corresponding author: Dimitri Mugnai

Dedicated to Vicentiu, on the occasion of his 60th birthday, with sincere friendship and esteem

Received  June 2017 Revised  November 2017 Published  August 2018

Fund Project: The first author is member of the INDAM Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA). Her research is supported by the 2017 INdAM-GNAMPA Project Comportamento asintotico e controllo di equazioni di evoluzione non lineari. The second author is member of the INDAM Gruppo Nazionale per l'Analisi Matematica, la Probabilità a e le loro Applicazioni (GNAMPA). His research is supported by the 2017 INdAM-GNAMPA Project Equazioni Differenziali Non Lineari and by the M.I.U.R. project Variational methods, with applications to problems in mathematical physics and geometry (2015KB9WPT 009)

We consider a nonlinear elliptic equation with Robin boundary condition driven by the p-Laplacian and with a reaction term which depends also on the gradient. By using a topological approach based on the Leray-Schauder alternative principle, we show the existence of a smooth solution.

Citation: Genni Fragnelli, Dimitri Mugnai, Nikolaos S. Papageorgiou. Robin problems for the p-Laplacian with gradient dependence. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 287-295. doi: 10.3934/dcdss.2019020
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