## Abstract

This paper presents an abstract theory for the existence, localization and multiplicity of fixed points in a cone. The key assumption is the property of the nonlinear operator of satisfying an inequality of Harnack type. In particular, the theory offers a completely new approach to the problem of positive solutions of quasilinear elliptic equations with *p*-Laplace operator.

## Authors

**Radu Precup**

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

## Keywords

Weak Harnack inequality; fixed point; fixed point index; p-Laplace operator; quasilinear elliptic equation.

## Paper coordinates

R. Precup, *Abstract weak Harnack inequality, multiple fixed points and p-Laplace equations*, J. Fixed Point Theory Appl. 12 (2012), 193-206, https://doi.org/10.1007/s11784-012-0091-2

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## About this paper

##### Journal

Journal of Fixed Point Theory and Applications

##### Publisher Name

Springer

##### Print ISSN

##### Online ISSN

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