## Abstract

The paper presents an abstract theory regarding operator equations and systems in ordered Banach spaces. We obtain existence, localization and multiplicity results of positive solutions using Krasnosel’skii’s fixed point theorem in cones, and a Harnack type inequality. Concerning systems, the localization is established by the vector version of Krasnosel’skii’s theorem, where the compression-expansion conditions are expressed on components. The approach is sufficiently general to cover and unify a large number of results on particular classes of problems. It also can guide future research in this direction.

## Authors

Diana-Raluca** Herlea
**Babeș-Bolyai University, Cluj-Napoca, Romania

Donal **O’Regan
**National University of Ireland, Galway, Ireland

Radu **Precup**

Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

Boundary value problem; positive solution; Harnack inequality; Krasnosel’skii’s fixed point theorem in cones; operator equation

## Paper coordinates

D.-R. Herlea, D. O’Regan, R. Precup, *Harnack type inequalities and multiple solutions in cones of nonlinear problems*, Z. Anal. Anwend. 39 (2020), 151-170, https://doi.org/10.4171/zaa/1655

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## About this paper

##### Journal

Zeitschrift fur Analysis und ihre Anwendunge

##### Publisher Name

EMS

European Mathematical Society

##### Print ISSN

0232-2064

##### Online ISSN

1661-4534

google scholar link

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