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| 摘要: |
本文研究了二阶离散周期边值问题
Δ2u（t-1）+f（t，u（t），Δu（t-1））=s，t∈[1，T]Z，
u（0）-u（T）=Δu（0）-Δu（T）=0
解的个数与参数s的关系，其中f（t，u，v）：[1，T]Z×R2→R关于（u，v）∈R2连续，s∈R.利用上下解方法和拓扑度理论，获得了Ambrosetti-Prodi型结果，推广了已有文献的相关结果. |
| 关键词: 二阶周期边值问题 Ambrosetti-Prodi型结果 上下解方法 拓扑度理论 |
| DOI： |
| 分类号:O175.8 |
| 基金项目:国家自然科学基金资助（12061064），西北师范大学研究生科研资助（2020KYZZ001109）. |
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| AMBROSETTI-PRODI TYPE RESULTS FOR NONLINEAR SECOND-ORDER DISCRETE PERIODIC BOUNDARY VALUE PROBLEMS |
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ZHAO Jiao
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| Abstract: |
In this paper, we discuss the relationship between the number of the solutions for second-order discrete periodic boundary value problem
Δ2u(t-1)+f(t, u(t), Δu(t-1))=s, t∈[1, T]Z,
u(0) -u(T)=Δu(0)-Δu(T)=0
and the parameter s, where f(t, u, v):[1, T]Z×R2→R is continuous with respect to (u, v)∈R2, s∈R. By using the method of the upper and lower solutions and topological degree techniques, Ambrosetti-Prodi type result is obtained, and some related conclusions on this topic are generalized. |
| Key words: second-order periodic BVPs Ambrosetti-Prodi type results upper and lower solutions topological degree techniques |
