一类分数阶方程山路解的存在性  

Existence of Mountain Pass Solutions for a Class of Fractional Equations

作　　者：许尔伟 张琦琦 XU Er-wei;ZHANG Qi-qi(School of Information Engineering,Lanzhou City University,Lanzhou Gansu 730070)

机构地区：[1]兰州城市学院信息工程学院,甘肃兰州730070

出　　处：《甘肃高师学报》2023年第5期10-13,共4页Journal of Gansu Normal Colleges

摘　　要：文章在Rn的有界区域上考察了一类含有临界增长非线性项的分数阶问题,并分析了问题所对应的变分泛函的结构.在次临界项前的函数满足合适的有界性条件下,根据泛函具有的山路结构和在山路水平处满足(PS)条件的论证,问题得到了一个非平凡的山路解.文章获得的结论是对有界区域上含有临界增长非线性项分数阶问题解的存在性研究的有效补充.The paper considered a class of fractional problems with critical growth nonlinearity on a bounded domain of R",and analyzed the structure of the variational functional corresponding to the problem.If the function before the subcritical term satisfies suitable bounded conditions,we prove that the problem has a non-trivial mountain pass solution according to the functional has mountain pass geometry and satisfies the(PS)condition at the mountain pass level.The conclusion obtained in this paper is an effective supplement to the study of existence of solution for fractional problems with critical growth nonlinear terms in bounded domain of R".

关 键 词：分数阶问题 有界区域 山路解 

分 类 号：O177.91[理学—数学]