Abstract
In this paper, we are concerned with positive solutions for the Dirichlet boundary value problem for equations and systems of Kirchhoff type. We obtain existence and localization results of positive solutions using Krasnosel’skiĭ’s fixed point theorem in cones and a weak Harnack-type inequality. The localization is given in terms of energy norm, being of interest from a physical point of view. In the case of systems, the results on the localization are established componentwise using the vector version of Krasnosel’skiĭ’s theorem, which allows some of the equations of the system to satisfy the compression condition and others the expansion one.
Authors
Nataliia Kolun
Department of Fundamental Sciences, Military Academy, 65009 Odessa, Ukraine
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania
Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Kirchhoff equation; positive solution; Dirichlet boundary value problem; Krasnosel’skiĭ’s fixed point theorem in a cone; weak Harnack inequality
Paper coordinates
Energy-based localization of positive solutions for stationary Kirchhoff-type equations and systems, Georgian Math. J., https://doi.org/10.1515/gmj-2023-2039
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About this paper
Print ISSN
1572-9176
Online ISSN
1072-947X
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