Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory

In this paper, we show that the bifurcation points for a discrete Kirchhoff-type problem with only local conditions, and we investigate the existence of positive and negative solutions for the problem when the nonlinear term \(f\) is asymptotically linear at zero and is asymptotically 3-linear at in...

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Main Author: Fumei Ye
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2025-07-01
Series:Opuscula Mathematica
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Online Access:https://www.opuscula.agh.edu.pl/vol45/4/art/opuscula_math_4526.pdf
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author Fumei Ye
author_facet Fumei Ye
author_sort Fumei Ye
collection DOAJ
description In this paper, we show that the bifurcation points for a discrete Kirchhoff-type problem with only local conditions, and we investigate the existence of positive and negative solutions for the problem when the nonlinear term \(f\) is asymptotically linear at zero and is asymptotically 3-linear at infinity. By using bifurcation techniques and the idea of taking limits of connected branches, under the assumption that \(f\) has some non-zero zeros, some results are also obtained.
format Article
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publisher AGH Univeristy of Science and Technology Press
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spelling doaj-art-7a12bfdf9dac4e2eada504a4ab655ae42025-08-20T03:11:57ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742025-07-01454559573https://doi.org/10.7494/OpMath.2025.45.4.5594526Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theoryFumei Ye0https://orcid.org/0000-0003-1754-308XSchool of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, ChinaIn this paper, we show that the bifurcation points for a discrete Kirchhoff-type problem with only local conditions, and we investigate the existence of positive and negative solutions for the problem when the nonlinear term \(f\) is asymptotically linear at zero and is asymptotically 3-linear at infinity. By using bifurcation techniques and the idea of taking limits of connected branches, under the assumption that \(f\) has some non-zero zeros, some results are also obtained.https://www.opuscula.agh.edu.pl/vol45/4/art/opuscula_math_4526.pdfdiscrete kirchhoff-type problemnontrivial solutionbifurcationsuperior limit
spellingShingle Fumei Ye
Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory
Opuscula Mathematica
discrete kirchhoff-type problem
nontrivial solution
bifurcation
superior limit
title Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory
title_full Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory
title_fullStr Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory
title_full_unstemmed Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory
title_short Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory
title_sort nontrivial solutions of discrete kirchhoff type problem via bifurcation theory
topic discrete kirchhoff-type problem
nontrivial solution
bifurcation
superior limit
url https://www.opuscula.agh.edu.pl/vol45/4/art/opuscula_math_4526.pdf
work_keys_str_mv AT fumeiye nontrivialsolutionsofdiscretekirchhofftypeproblemviabifurcationtheory