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浙江大学学报（理学版）
浙江大学学报（理学版）  2020, Vol. 47 Issue (5): 535-540    DOI: 10.3785/j.issn.1008-9497.2020.05.003
数学与计算机科学     
一类分数阶p（x）-拉普拉斯方程的多重解
张申贵
西北民族大学 数学与计算机科学学院，甘肃 兰州 730030
Multiple solutions of a class of fractional p(x)-Laplacian equations
ZHANG Shengui
College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
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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。
关键词： 次线性;  超线性;  分数阶p（x）-拉普拉斯方程;  临界点    
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.
Key words: sublinear    superlinear    fractional p(x)-Laplacian equation    critical point
收稿日期: 2018-04-08 出版日期: 2020-09-25
CLC:  O175.8  
基金资助: 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).
通讯作者: E-mail：zhangshengui315@163.com.     E-mail: zhangshengui315@163.com
作者简介: 张申贵(1980—)，ORCID: http://orcid.org/0000-0002-4381-9927，男，博士，副教授，主要从事非线性泛函分析研究,。
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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）, 2020, 47(5): 535-540.

ZHANG Shengui. Multiple solutions of a class of fractional p(x)-Laplacian equations. Journal of Zhejiang University (Science Edition), 2020, 47(5): 535-540.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.05.003    或    https://www.zjujournals.com/sci/CN/Y2020/V47/I5/535

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