## Abstract

In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational, quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework for the existence of fixed points of nonlinear operators acting on cones that satisfy an inequality of Harnack type. Our methodology relies on fixed point index theory. We also provide a non-existence result and an example to illustrate the theory.

## Authors

**Radu Precup**

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

weak Harnack inequality; fixed point index; p-Laplace operator; quasilinear elliptic system; positive weak solution; cone; multiplicity; nonexistence

## Paper coordinates

G. Infante, M. Maciejewski, R. Precup, *A topological approach to the existence and multiplicity of positive solutions of (p,q)-Laplacian systems*, Dyn. Partial Differ. Equ. 12 (2015), no.3, 193-215, http://dx.doi.org/10.4310/DPDE.2015.v12.n3.a1

## About this paper

##### Journal

Dynamics of Partial Differential Equations

##### Publisher Name

##### Print ISSN

1548159X

##### Online ISSN

21637873

google scholar link

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