| 摘要: |
| 本文研究了一类分数阶p（x）-Laplace算子方程解的存在性和多解性问题.在非线性项不满足（AR）条件时，利用喷泉定理和分数阶变指数Sobolev空间的相关理论，得到了方程无穷多解的存在性.从而推广了经典变指数问题的相关结果. |
| 关键词: 分数阶p(x)-Laplace方程 分数变指数Sobolev空间 喷泉定理 多解性 |
| DOI： |
| 分类号:O175.29 |
| 基金项目: |
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| MULTIPLICITY OF SOLUTIONS FOR A FRACTIONAL p(x)-LAPLACIAN EQUATION |
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ZHANG Jin-guo1, JIAO Hong-ying2,3, LIU Qiu-yun1
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1.Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China;2.Department of Basic Sciences, Air Force Engineering University, Xi'an 710051, China;3.School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
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| Abstract: |
| In this paper, we investigate the existence and multiplicity of solutions to a class of fractional p(x)-Laplacian equation. By means of Fountain theorem and the theory of fractional variable exponent Sobolev space, we show that the equation has a sequence of nontrivial solutions with high energies, which generalize the results of classical variable exponent problem. |
| Key words: fractional p(x)-Laplacian operator fractional variable exponent Sobolev space fountain theorem multiple solutions |
