AMBROSETTI-PRODI TYPE RESULTS FOR DISCRETE MINKOWSKI-MEAN CURVATURE OPERATORS WITH REPULSIVE SINGULARITIES

Yaqin Li; Yanqiong Lu

doi:10.11948/20240502

2025 Volume 15 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(5): 2726-2746

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Yaqin Li, Yanqiong Lu. AMBROSETTI-PRODI TYPE RESULTS FOR DISCRETE MINKOWSKI-MEAN CURVATURE OPERATORS WITH REPULSIVE SINGULARITIES[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2726-2746. doi: 10.11948/20240502

Citation:

Yaqin Li, Yanqiong Lu. AMBROSETTI-PRODI TYPE RESULTS FOR DISCRETE MINKOWSKI-MEAN CURVATURE OPERATORS WITH REPULSIVE SINGULARITIES[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2726-2746. doi: 10.11948/20240502

AMBROSETTI-PRODI TYPE RESULTS FOR DISCRETE MINKOWSKI-MEAN CURVATURE OPERATORS WITH REPULSIVE SINGULARITIES

Yaqin Li^1,,
Yanqiong Lu^1, ,

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, Gansu, China

Author Bio: Email: 18919454637@163.com(Y. Li)
Corresponding author: Email: luyq8610@126.com(Y. Lu)
Fund Project: Supported by National Natural Science Foundation of China (No. 12361040)

Abstract

Abstract

In this work, we study an Ambrosetti-prodi type results for discrete Minkowski-mean curvature operators with repulsive singularities
$ \begin{align*} &\triangle\Big(\frac{\triangle u(t-1)}{\sqrt{1-(\triangle u(t-1))^{2}}}\Big)+f(u)\triangle u(t)+g(t,u (t))=s,\quad t\in[1,T]_{\mathbb{Z}},\nonumber\\ &u(0)=u(T),\quad \triangle u(0)=\triangle u(T), \end{align*} $
where $ f:(0,+\infty)\rightarrow \mathbb{R} $ is a continuous $ T $-periodic function, $ g:[1,T]_{\mathbb{Z}}\times(0,+\infty)\rightarrow \mathbb{R} $ is a continuous $ T $-periodic function with a repulsive singularity at the origin, and $ s\in \mathbb{R} $ is a parameter, $ T\geq2 $ is integer.
- Repulsive singular /
- Ambrosetti-Prodi type results /
- degree theory /
- Liénard equation /
- continuation theorem
MSC: 34B08, 34C25

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References

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