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Nontrivial solutions of discrete Kirchhoff-type problem via bifurcation theory

Ye Fumei

Opuscula Mathematica

2025

Vol. 45, no. 4

559--573

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 ƒ 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 ƒ has some non-zero zeros, some results are also obtained.