# American Institute of Mathematical Sciences

April  2018, 11(2): 293-307. doi: 10.3934/dcdss.2018016

## Location of Nodal solutions for quasilinear elliptic equations with gradient dependence

 1 Université de Perpignan, Département de Mathématiques, 66860 Perpignan, France 2 Lycée Polyvalent Franklin Roosevelt, 10 Rue du Président Franklin Roosevelt, 51100 Reims, France 3 Université A. Mira de Bejaia, Laboratoire de Mathématiques Appliquées (LMA), Faculté des Sciences Exactes, Targa Ouzemour 06000 Bejaia, Algeria

* Corresponding author: Dumitru Motreanu

Received  August 2016 Revised  April 2017 Published  January 2018

Existence and regularity results for quasilinear elliptic equations driven by $(p, q)$-Laplacian and with gradient dependence are presented. A location principle for nodal (i.e., sign-changing) solutions is obtained by means of constant-sign solutions whose existence is also derived. Criteria for the existence of extremal solutions are finally established.

Citation: Dumitru Motreanu, Viorica V. Motreanu, Abdelkrim Moussaoui. Location of Nodal solutions for quasilinear elliptic equations with gradient dependence. Discrete & Continuous Dynamical Systems - S, 2018, 11 (2) : 293-307. doi: 10.3934/dcdss.2018016
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