[1]黄 红,尚旭东.一类含对数非线性项的分数阶基尔霍夫型方程解的存在性[J].南京师大学报(自然科学版),2023,46(01):24-27.[doi:10.3969/j.issn.1001-4616.2023.01.005]
　Huang Hong,Shang Xudong.Existence of Solution for a Kind of Fractional Kirchhoff Equation with Logarithmic Nonlinearity[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(01):24-27.[doi:10.3969/j.issn.1001-4616.2023.01.005]
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一类含对数非线性项的分数阶基尔霍夫型方程解的存在性()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第46卷
期数:
2023年01期
页码:
24-27
栏目:
数学
出版日期:
2023-03-15

文章信息/Info

Title:
Existence of Solution for a Kind of Fractional Kirchhoff Equation with Logarithmic Nonlinearity
文章编号:
1001-4616(2023)01-0024-04
作者:
黄 红1; 尚旭东2
(1.南京师范大学中北学院，江苏 镇江 212334)
(2.南京师范大学泰州学院，江苏 泰州 225300)
Author(s):
Huang Hong1; Shang Xudong2
(1.Zhongbei College, Nanjing Normal University, Zhenjiang 212334, China)
(2.Taizhou College, Nanjing Normal University, Taizhou 225300, China)
关键词:
分数阶基尔霍夫型方程; 对数非线性项; 紧性条件; 山路引理
Keywords:
fractional Kirchhoff equation;  logarithmic nonlinearity;  compactness condition;  mountain pass lemma
分类号:
O175.8
DOI:
10.3969/j.issn.1001-4616.2023.01.005
文献标志码:
A
摘要:
通过对对数项精细的估计来证明紧性条件的成立,借助山路引理,研究带有对数非线性项的分数阶基尔霍夫型方程

在一定条件下解的存在性.
Abstract:
By proving the compactness condition through careful estimation of logarithmic terms,and with the help of mountain pass lemma,the authors study the existence of nontrivial solution for a kind of fractional Kirchhoff equation with logarithmic nonlinear term

under certain conditions.

参考文献/References:

[1]KIRCHHOFF G. Vorlesungen Uber Mechanik,Teubner,Leipzig[M]. Stutgarty:Springer,1883.
[2]PERERA K,ZHANG Z. Nontrivial solutions of Kirchhoff-type problems via the Yang index[J]. Journal of differential equations,2006,221:246-255.
[3]CHEN C Y,KUO Y C,WU T F. The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions[J]. Journal of differential equations,2011,250:1876-1908.
[4]FISCELLA A,VALDINOCI E. A critical Kirchhoff type problem involving a nonlocal operator[J]. Nonlinear analysis,2014,94:156-170.
[5]PUCCI P,XIANG M Q,ZHANG B L. Existence of entire solutions for Kirchhoff type equations involving the fractional p-Laplacian[J]. Advances in nonlinear analysis,2016,5:27-55.
[6]XIANG M Q,PUCCI P,SQUASSINA M,et al. Nonlocal Schr?inger Kirchhoff equations with external magnetic field[J]. Discrete and continuous dynamical systems,2017,37:503-521.
[7]SONG Y Q,SHI S Y. Existence of infinitely many solutions for degenerate p-fractional Kirchhoff equations with critical Sobolev-Hardy nonlinearities[J]. Zeitschrift fur angewandte mathematik und physik,2017,68:1-13.
[8]D’AVENIA P,SQUASSINA M,ZENARI M. Fractional logarithmic Schr?inger equations[J]. Mathematical methods in the applied sciences,2015,38:5207-5216.
[9]TRUONG L X. The Nehari manifold for fractional p-Laplacian equation with logarithmic nonlinearity on whole space[J]. Computers and mathematics with applications,2019,78:3931-3940.
[10]DI NEZZA E,PALATUCCI G,VALDINOCI E. Hitchhiker’s guide to the fractional Sobolev spaces[J]. Bulletin des sciences mathématiques,2012,136:521-573.
[11]RABINOWITZ P H. Minimax methods in critical point theory with applications to diferential equations[M]. Providence,Rhode Island:American Mathematical Society,1984.

备注/Memo

备注/Memo:
收稿日期:2022-06-19.
基金项目:国家自然科学基金资助项目(11571176,11701289).
通讯作者:尚旭东,博士,副教授,研究方向:非线性分析,临界点理论及对非线性偏微分方程的应用. E-mail:xudong-shang@163.com
更新日期/Last Update: 2023-03-15