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
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