| 一维$P$-Laplace二阶差分系统奇异边值问题正解的存在性 |
| |
| 引用本文： | 胡卫敏,巴哈尔古丽,蒋达清. 一维$P$-Laplace二阶差分系统奇异边值问题正解的存在性[J]. 数学研究及应用, 2013, 33(2): 189-203 |
| |
| 作者姓名： | 胡卫敏 巴哈尔古丽 蒋达清 |
| |
| 作者单位： | 伊犁师范学院数学与统计学院, 新疆 伊宁835000;伊犁师范学院数学与统计学院, 新疆 伊宁835000;东北师范大学数学与统计学院, 吉林 长春 130024 |
| |
| 基金项目： | 新疆普通高校重点培育学科开放课题(Grant No.XJZDXK2011004),国家自然科学基金(Grant No.10971021). |
| |
| 摘 要： | 应用锥压缩锥拉伸不动点定理和Leray-Schauder 抉择定理研究了一类具有P-Laplace算子的奇异离散边值问题$$left{begin{array}{l}Delta[phi (Delta x(i-1))]+ q_{1}(i)f_{1}(i,x(i),y(i))=0, ~~~iin {1,2,...,T}Delta[phi (Delta y(i-1))]+ q_{2}(i)f_{2}(i,x(i),y(i))=0,x(0)=x(T+1)=y(0)=y(T+1)=0,end{array}right.$$的单一和多重正解的存在性，其中$phi(s) = |s|^{p-2}s, ~p>1$，非线性项$f_{k}(i,x,y)(k=1,2)$在$(x,y)=(0,0)$具有奇性.
|
| 关 键 词： | 分数阶微分方程 格林函数 正解 不动点定理 边值问题. |
| 收稿时间： | 2011-12-15 |
| 修稿时间： | 2012-10-12 |
Existence of Positive Solutions for Singular One-Dimensional $P$-Laplace BVP of the Second-Order Difference Systems |
| |
| Weimin HU,Guli Bahaer and Daqing JIANG. Existence of Positive Solutions for Singular One-Dimensional $P$-Laplace BVP of the Second-Order Difference Systems[J]. Journal of Mathematical Research with Applications, 2013, 33(2): 189-203 |
| |
| Authors: | Weimin HU Guli Bahaer Daqing JIANG |
| |
| Affiliation: | School of Mathematics and Statistics, Ili Normal University, Xinjiang 835000, P. R. China;School of Mathematics and Statistics, Ili Normal University, Xinjiang 835000, P. R. China;School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China |
| |
| Abstract: | In this paper we establish the existence of single and multiple positive solutions to the following singular discrete boundary value problem $$left{begin{array}{l}Delta[phi (Delta x(i-1))]+ q_{1}(i)f_{1}(i,x(i),y(i))=0, ~~iin {1,2,ldots,T}Delta[phi (Delta y(i-1))]+ q_{2}(i)f_{2}(i,x(i),y(i))=0,x(0)=x(T+1)=y(0)=y(T+1)=0,end{array}right.tag 1.1$$ where $phi(s)=|s|^{p-2}s$, $p>1$ and the nonlinear terms $f_{k}(i,x,y)~(k=1,2)$ may be singular at $(x,y)=(0,0)$. |
| |
| Keywords: | multiple solutions singular existence discrete boundary value problem. |
|
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
|
点击此处可从《数学研究及应用》下载全文 |
|
