| 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) , tin [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： | 2022-02-28 |
| 修稿时间： | 2022-08-19 |
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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| Affiliation: | 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 $$left{begin{array}{ll}-Delta^{2} u(t-1)=lambda g(t)f(u), &tin [1,T]_mathbb{Z},u(0)=0, Delta u(T)+c(u(T+1))u(T+1)=0,end{array}right.$$ 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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