| 一类分数阶p（x）-拉普拉斯方程的多重解 |
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| 引用本文： | 张申贵. 一类分数阶p（x）-拉普拉斯方程的多重解[J]. 浙江大学学报(理学版), 2021, 47(5): 535-540. DOI: 10.3785/j.issn.1008-9497.2020.05.003 |
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| 作者姓名： | 张申贵 |
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| 基金项目： | 国家自然科学基金资助项目(11401473)；中央高校基本科研业务专项经费项目(31920180041, 31920180047). |
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| 摘 要： | 利用临界点理论、变分方法和分数阶变指数Sobolev空间理论, 研究带有非局部系数的分数阶p(x)-拉普拉斯方程边值问题的可解性。当非线性项在零点附近次线性或在无穷远处局部超线性增长时, 得到了此类问题多重解存在的充分条件。
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| 关 键 词： | 分数阶p（x）-拉普拉斯方程 临界点 次线性 超线性 |
| 收稿时间： | 2018-04-08 |
Multiple solutions of a class of fractional p(x)-Laplacian equations |
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| ZHANG Shengui. Multiple solutions of a class of fractional p(x)-Laplacian equations[J]. Journal of Zhejiang University(Sciences Edition), 2021, 47(5): 535-540. DOI: 10.3785/j.issn.1008-9497.2020.05.003 |
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| Authors: | ZHANG Shengui |
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| Affiliation: | College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China |
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| Abstract: | By using the critical point theory, variational methods and the theory of fractional variable exponent Sobolev space, this paper studies the solvability of the boundary value problem of fractional p(x)-Laplacian equation with nonlocal coefficient. When the nonlinearity item is sublinear near zero or local superlinear at infinity, some sufficient condition for the existence of multiple solutions are obtained. |
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| Keywords: | fractional p(x)-Laplacian equation critical point sublinear superlinear |
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