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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| Format: | Article |
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AGH Univeristy of Science and Technology Press
2025-07-01
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| 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 |
| id | doaj-art-7a12bfdf9dac4e2eada504a4ab655ae4 |
| institution | DOAJ |
| issn | 1232-9274 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| 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 |