GLOBAL BIFURCATION RESULT FOR DISCRETE BOUNDARY VALUE PROBLEM INVOLVING THE MEAN CURVATURE OPERATOR

Fumei Ye; Xiaoling Han

doi:10.11948/20200386

2021 Volume 11 Issue 5

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Fumei Ye, Xiaoling Han. GLOBAL BIFURCATION RESULT FOR DISCRETE BOUNDARY VALUE PROBLEM INVOLVING THE MEAN CURVATURE OPERATOR[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2355-2362. doi: 10.11948/20200386

Citation:

Fumei Ye, Xiaoling Han. GLOBAL BIFURCATION RESULT FOR DISCRETE BOUNDARY VALUE PROBLEM INVOLVING THE MEAN CURVATURE OPERATOR[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2355-2362. doi: 10.11948/20200386

GLOBAL BIFURCATION RESULT FOR DISCRETE BOUNDARY VALUE PROBLEM INVOLVING THE MEAN CURVATURE OPERATOR

Fumei Ye^1, ,,
Xiaoling Han^1, ,

1.
School of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China

Corresponding authors: Email: yfm_nwnu@163.com(F. Ye); Email: hanxiaoling@nwnu.edu.cn(X. Han)
Fund Project: The authors were supported by Natural Science Foundation of Gansu Province (20JR10RA086)

Abstract

Abstract

In this paper, by applying bifurcation technique, we obtain that there are two distinct unbounded continua $ \mathcal{C}_k^+ $ and $ \mathcal{C}_k^- $ for a class of discrete Dirichlet problem involving the mean curvature operator which bifurcate from intervals of the line of trivial solutions. Under some suitable conditions on nonlinear term near at the origin, we will show the existence and multiplicity of nontrivial solutions.
- Singular ϕ-Laplacian /
- interval bifurcation /
- difference equation
MSC: 39A06, 39A27, 39A28, 47J10

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References

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