Journal of Guangxi Normal University(Natural Science Edition) ›› 2020, Vol. 38 ›› Issue (6): 65-73.doi: 10.16088/j.issn.1001-6600.2020.06.008

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Infinitely Many Classical Solutions for Kirchhoff Type Problem with Linear Term

WANG Yue1, YE Hongyan2, LEI Jun2, SUO Hongmin2*   

  1. 1. School of Mathematics and Statistics, Guizhou University, Guiyang Guizhou 550025, China;
    2. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang Guizhou 550025, China
  • Received:2019-05-15 Published:2020-11-30

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Abstract: Nonlocal Kirchhoff type problem with linear exponent on Neumann’s boundary condition are considered in this paper. Infinitely many classical solutions {un}∞n=1 are obtained by using constructors of special functions and partial discussion, where un→0 as n→+∞. In terms of variation methods, for those solutions, the energies of corresponding functional are converged to a nonzero constant. Moreover the energies of corresponding functional are converged to zero for the solutions near resonances in this problem. All results mentioned above are suitable for Dirichlet’s boundary condition.

Key words: infinitely many classical solutions, linear exponent, nonlocal problem, constructor of function, near resonance

CLC Number: 

  • O175.23
[1] KIRCHHOFF G R. Vorlesungen Über Matematische Physik:Mechanik[M]. Leipzig:Druck und von B G Teubner,1876:429-470.
[2] 王跃. 一类非局部问题解的存在性与多重性研究[D]. 贵阳:贵州民族大学,2018.
[3] WANG Y,SUO H M,LEI C Y. Multiple positive solutions for a nonlocal problem involving critical exponent[J/OL]. Electronic Journal of Differential Equations,2017,2017:275[2019-05-15]. http://ejde.math.unt.edu/Volumes/2017/275/wang.pdf.
[4] 贾秀玲,段誉. 一类带线性项非局部问题解的存在性与非存在性[J]. 西南师范大学学报(自然科学版),2018,43(10):22-25. DOI:10.13718/j.cnki.xsxb.2018.10.006.
[5] 蔡志鹏,储昌木,雷春雨. 一类非局部问题正解的存在性与多重性[J]. 重庆师范大学学报(自然科学版),2018,35(1):84-87. DOI:10.11721/cqnuj20180112.
[6] 王跃,梁金平,索洪敏. 一类非局部近共振问题多重解的存在性[J]. 西南大学学报(自然科学版),2018,40(4):53-58. DOI:10.13718/j.cnki.xdzk.2018.04.009.
[7] 梁金平,索洪敏,雷春雨. 一类含临界指数和凹项的非局部问题多重正解的存在性[J]. 应用数学,2019,32(1):39-44. DOI:10.13642/j.cnki.42-1184/o1.2019.01.005.
[8] 王跃,叶红艳,索洪敏. 一类带Hardy-Sobolev临界指数的非局部问题正解的存在性[J]. 应用数学,2019,32(2):452-456. DOI:10.13642/j.cnki.42-1184/o1.2019.02.042.
[9] ZHANG J,ZHANG Z Y. Existence of nontrivial solution for a nonlocal problem with subcritical nonlinearity[J]. Advances in Difference Equations,2018,2018:359. DOI:10.1186/s13662-018-1823-4.
[10] LEI C Y,LIAO J F,SUO H M. Multiple positive solutions for nonlocal problems involving a sign-changing potential[J/OL]. Electronic Journal of Differential Equations,2017,2017:9[2019-05-15]. http://ejde.math.unt.edu/Volumes/2017/09/lei.pdf.
[11] LEI C Y,CHU C M,SUO H M. Positive solutions for a nonlocal problem with singularity[J/OL]. Electronic Journal of Differential Equations,2017,2017:85[2019-05-15]. http://ejde.math.unt.edu/Volumes/2017/85/lei.pdf.
[12] YIN G S,LIU J S. Existence and multiplicity of nontrivial solutions for a nonlocal problem[J]. Boundary Value Problems,2015,2015:26. DOI:10.1186/s13661-015-0284-x.
[13] 陆文端. 微分方程中的变分方法:修订版[M]. 北京:科学出版社,2003:156-161.
[14] STRAUSS W A. Partial differential equations an introduction[M]. 2nd ed. New Jersey: John Wiley &Sons Ltd,2007:299-330.
[15] 王跃,杨训,刘臣伟,等. Kirchhoff型问题多个解的存在性及表示[J]. 湖北民族学院学报(自然科学版),2019,37(2):165-168. DOI:10.13501/j.cnki.42-1569/n.2019.06.010.
[16] 丁凌,汪继秀,肖氏武. 全空间上具有临界指数的Kirchhoff 类方程无穷多个正解的存在性[J]. 南昌大学学报(理科版),2017,41(5):414-417. DOI:10.3969/j.issn.1006-0464.2017.05.002.
[17] 王跃,梁金平,索洪敏,等. 非局部问题在不同无界域下的古典解[J]. 应用泛函分析学报,2019,21(4):325-341. DOI:10.12012/1009-1327(2019)04-0325-17.
[18] 王跃,索洪敏,韦维. 无边界约束的一类新Kirchhoff型问题的古典解[J]. 数学物理学报:A辑,2020,40(4):857-868.
[19] HAMDANI M K,HARRABI A,MTIRI F,et al. Existence and multiplicity results for a new p(x)-Kirchhoff problem[J]. Nonlinear Analysis,2020,190:111598. DOI:10.1016/j.na.2019.111598.
[20] 王跃,周荧,索洪敏,等. 关于一类临界Kirchhoff问题的解[J]. 成都理工大学学报(自然科学版),2020,47(2):245-248. DOI:10.3969/j.issn.1671-9727.2020.02.13.
[21] 闫荣君,韦煜明,冯春华. 带p-Laplacian算子的时滞分数阶微分方程边值问题3个正解的存在性[J]. 广西师范大学学报(自然科学版),2017,35(3):75-82. DOI:10.16088/j.issn.1001-6600.2017.03.009.
[22] 黄燕萍,韦煜明. 一类分数阶微分方程多点边值问题的多解性[J]. 广西师范大学学报(自然科学版),2018,36(3):41-49. DOI:10.16088/j.issn.1001-6600.2018.03.006.
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