Opuscula Math. 45, no. 4 (2025), 559-573
https://doi.org/10.7494/OpMath.2025.45.4.559
Opuscula Mathematica
Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory
Abstract. 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.
Keywords: discrete Kirchhoff-type problem, nontrivial solution, bifurcation, superior limit.
Mathematics Subject Classification: 39A05, 39A28, 34B15.
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- Fumei Ye
https://orcid.org/0000-0003-1754-308X- School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China
- Communicated by Vicenţiu D. Rădulescu.
- Received: 2025-04-21.
- Revised: 2025-05-27.
- Accepted: 2025-05-28.
- Published online: 2025-07-16.
