| 非线性边界条件下二阶奇异差分方程的正解 |
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| 引用本文： | 李慧娟,Alhussein MOHAMED,高承华.非线性边界条件下二阶奇异差分方程的正解[J].数学研究及应用,2023,43(1):101-108. |
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| 作者姓名： | 李慧娟 Alhussein MOHAMED 高承华 |
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| 作者单位： | 西北师范大学数学与统计学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金(Grant No.11961060). |
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| 摘 要： | 本文我们考虑如下二阶奇异差分边值问题\begin{equation*}\begin{cases}-\Delta^{2} u(t-1)=\lambda g(t)f(u) ,\ t\in 1,T]_\mathbb{Z},\\u(0)=0,\\ \Delta u(T)+c(u(T+1))u(T+1)=0,\end{cases}\end{equation*}正解的存在性. 其中, $\lambda>0$, $f:(0,\infty)\rightarrow \mathbb{R}$ 是连续的,且允许在~$0$ 处奇异.通过引入一个新的全连续算子, 我们建立正解的存在性.
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| 关 键 词： | 差分方程 非线性边界条件 正解 |
| 收稿时间： | 2022/2/28 0:00:00 |
| 修稿时间： | 2022/8/19 0:00:00 |
Positive Solutions for Second-Order Singular Difference Equation with Nonlinear Boundary Conditions |
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| Huijuan LI,Alhussein MOHAMED,Chenghua GAO.Positive Solutions for Second-Order Singular Difference Equation with Nonlinear Boundary Conditions[J].Journal of Mathematical Research with Applications,2023,43(1):101-108. |
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| Authors: | Huijuan LI Alhussein MOHAMED Chenghua GAO |
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| Institution: | Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China |
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| Abstract: | In this paper, we discuss the existence of positive solutions for the second-order singular difference equation boundary value problem $$\left\{\begin{array}{ll}-\Delta^{2} u(t-1)=\lambda g(t)f(u), &t\in 1,T]_\mathbb{Z},\\u(0)=0,\\ \Delta u(T)+c(u(T+1))u(T+1)=0,\end{array}\right.$$ where $\lambda>0$ is a positive parameter, $f:(0,\infty)\rightarrow \mathbb{R}$ is continuous, and is allowed to be singular at $0$. The existence of positive solutions is established via introducing a new complete continuous operator. |
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| Keywords: | difference equation nonlinear boundary conditions positive solutions |
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