Energy-based localization of positive solutions for stationary Kirchhoff-type equations and systems
-
Nataliia Kolun
and
Radu Precup
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.
Funding statement: This work is carried out within the “Yulia Zdanovska Postdoctoral Fellowship” project (CNFIS-FDI-2022-0179) of the Institute for Advanced Studies in Science and Technology at Babeş-Bolyai University of Cluj-Napoca, Romania.
Acknowledgements
The authors wish to thank the reviewer for careful reading of the manuscript and valuable comments that led to an improved version of the paper. The first author expresses her gratitude to the staff of Babeş-Bolyai University for all the support.
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Articles in the same Issue
- Frontmatter
- On left and right Browder elements in Banach algebra relative to a bounded homomorphism
- Uniform excess of g-frames
- On normal partial isometries
- Gauss--Newton--Kurchatov method for the solution of non-linear least-square problems using ω-condition
- Maps preserving the bi-skew Jordan product on factor von Neumann algebras
- Boundary contact problems with regard to friction of couple-stress viscoelasticity for inhomogeneous anisotropic bodies (quasi-static cases)
- On uniform statistical convergence
- Approximate solution of the optimal control problem for non-linear differential inclusion on the semi-axes
- Energy-based localization of positive solutions for stationary Kirchhoff-type equations and systems
- e-reversibility of rings via quasinilpotents
- Weighted generalized Moore–Penrose inverse
- On two extensions of the annihilating-ideal graph of commutative rings
- Umbral treatment and lacunary generating function for Hermite polynomials
- A generalization of the canonical commutation relation and Heisenberg uncertainty principle for the orbital operators
