Robin problems for the p-Laplacian with gradient dependence

Genni Fragnelli; Dimitri Mugnai; Nikolaos S. Papageorgiou

doi:10.3934/dcdss.2019020

Article Contents

2019, Volume 12, Issue 2: 287-295. Doi: 10.3934/dcdss.2019020

This issue Previous Article Existence of solutions for quasilinear Dirichlet problems with gradient terms Next Article On a class of mixed Choquard-Schrödinger-Poisson systems

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
* Corresponding author: Dimitri Mugnai

Received: June 2017

Revised: November 2017

Published: April 2019

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).

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J20; Secondary: 35J60, 35J92.

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References

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