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一类具有变号位势Kirchhoff型方程解的存在性

雷俊 索洪敏 彭林艳 吴德科 蒙璐

雷俊, 索洪敏, 彭林艳, 吴德科, 蒙璐. 一类具有变号位势Kirchhoff型方程解的存在性[J]. 应用数学和力学, 2021, 42(8): 859-865. doi: 10.21656/1000-0887.410283
引用本文: 雷俊, 索洪敏, 彭林艳, 吴德科, 蒙璐. 一类具有变号位势Kirchhoff型方程解的存在性[J]. 应用数学和力学, 2021, 42(8): 859-865. doi: 10.21656/1000-0887.410283
LEI Jun, SUO Hongmin, PENG Linyan, WU Deke, MENG Lu. Existence of Solutions for a Class of Kirchhoff Type Equations With SignChanging Potential[J]. Applied Mathematics and Mechanics, 2021, 42(8): 859-865. doi: 10.21656/1000-0887.410283
Citation: LEI Jun, SUO Hongmin, PENG Linyan, WU Deke, MENG Lu. Existence of Solutions for a Class of Kirchhoff Type Equations With SignChanging Potential[J]. Applied Mathematics and Mechanics, 2021, 42(8): 859-865. doi: 10.21656/1000-0887.410283

一类具有变号位势Kirchhoff型方程解的存在性

doi: 10.21656/1000-0887.410283
基金项目: 

国家自然科学基金(11661021;11861021)

详细信息
    作者简介:

    雷俊(1995—),男,硕士生(E-mail: 1769819417@qq.com);索洪敏(1965—),男,教授(通讯作者. E-mail: 11394861@qq.com).

    通讯作者:

    索洪敏(1965—),男,教授(通讯作者. E-mail: 11394861@qq.com).

  • 中图分类号: O176.3

Existence of Solutions for a Class of Kirchhoff Type Equations With SignChanging Potential

Funds: 

The National Natural Science Foundation of China(11661021;11861021)

  • 摘要: 该文研究了一类带有变号位势非线性项的Kirchhoff型方程的Neumann边值问题.利用变分方法,首先对空间进行分解,证明了该问题的能量泛函满足山路结构;然后证明了能量泛函的(PS)序列有强收敛的子列;最后通过Ekeland变分原理和山路引理,获得了该问题两个非平凡解的存在性.
  • [2]XIE W H, CHEN H B. Multiple positive solutions for the critical Kirchhoff type problems involving sign-changing weight functions[J]. Journal of Mathematical Analysis and Application,2019,479(1): 135-161.
    KIRCHHOFF G.Mechanik[M]. Leipzig: Teubner, 1883.
    [3]CAO X F, XU J X. Multiple solutions for Kirchhoff type problems involving super-linear and sub-linear terms[J].Electronic Journal of Qualitative Theory of Differential Equations,2015,16: 1-14.
    [4]SHEN L J, YAO X H. Multiple positive solutions for a class of Kirchhoff type problems involving general critical growth[R/OL]. 2016. (2016-07-07)[2021-03-12]. https://arxiv.org/pdf/1607.01923.pdf.
    [5]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(4): 1876-1908.
    [6]LIAO J F, LI H Y, ZHANG P. Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev exponent[J].Computers & Mathematics With Applications, 2018,75(3): 787-797.
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    [11]邵荣, 牛欣, 沈祖和. 非线性椭圆型边值问题解的存在性[J]. 应用数学和力学, 2003,24(1): 89-97.(SHAO Rong, NIU Xin, SHEN Zuhe. Existence of solutions for nonlinear elliptic boundary value problem[J].Applied Mathematics and Mechanics,2003,24(1): 89-97.(in Chinese))
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出版历程
  • 收稿日期:  2020-09-17
  • 修回日期:  2021-03-12
  • 网络出版日期:  2021-08-14

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