Harnack Type Inequalities and Multiple Solutions in Cones of Nonlinear Problems

  • Diana-Raluca Herlea

    Babeș-Bolyai University, Cluj-Napoca, Romania
  • Donal O'Regan

    National University of Ireland, Galway, Ireland
  • Radu Precup

    Babeș-Bolyai University, Cluj-Napoca, Romania
Harnack Type Inequalities and Multiple Solutions in Cones of Nonlinear Problems cover

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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.

Cite this article

Diana-Raluca Herlea, Donal O'Regan, Radu Precup, Harnack Type Inequalities and Multiple Solutions in Cones of Nonlinear Problems. Z. Anal. Anwend. 39 (2020), no. 2, pp. 151–170

DOI 10.4171/ZAA/1655