| 何延生,侯成敏.带有拉普拉斯算子的离散分数阶边值问题解的存在性[J].数学研究及应用,2014,34(2):197~208 |
| 带有拉普拉斯算子的离散分数阶边值问题解的存在性 |
| Existence of Solutions for Discrete Fractional Boundary Value Problems with p-Laplacian Operator |
| 投稿时间：2013-01-16 修订日期：2013-06-04 |
| DOI：10.3770/j.issn:2095-2651.2014.02.009 |
| 中文关键词: 分数阶差分 边值问题 变分框架 临界点定理. |
| 英文关键词:fractional difference boundary value problem variational framework critical point theory. |
| 基金项目:国家自然科学基金 (Grant No.11161049). |
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| 中文摘要: |
| 通过建立相应的变分框架并使用临界点定理,我们给出了带有P-Laplacian 算子的离散分数阶边值问题解的存在性.在适当的假设下,获得了使该问题至少存在3个解的正参数的存在性.几个例子表明了我们的主要结果. |
| 英文摘要: |
| By establishing the corresponding variational framework, and using the critical points theorem, we give the existence of multiple solutions for a fractional difference boundary value problem with $p$-Laplacian operator. Under some suitable assumptions we obtain the existence of a positive parameter such that the problem admits at least three solutions. Some examples are presented to illustrate the main results. |
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