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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