The paper presents an abstract theory regarding the problems with semilinear operator equations involving iterates of a strongly monotone symmetric linear operator. We obtain existence and localization results of positive solutions for such problems using Krasnosel’skiĭ’s technique and abstract Harnack inequality. In particular, we obtain results for problems with semilinear poly-Laplace operators.
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania
Krasnosel’skiĭ’s technique; fixed point; Harnack inequality; iterates of a symmetric linear operator. poly-Laplace type operator
N. Kolun, R. Precup, Localization of solutions for semilinear problems with poly-Laplace type operators, Applicable Analysis, published online 2023, https://doi.org/10.1080/00036811.2023.2218869
Applicable Analysis\Taylor & Francis Online
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