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

LEI Jun; SUO Hongmin; PENG Linyan; WU Deke; MENG Lu

doi:10.21656/1000-0887.410283

Volume 42 Issue 8

Aug. 2021

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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

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

doi: 10.21656/1000-0887.410283

School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, P.R.China

Funds:

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

Received Date: 2020-09-17
Rev Recd Date: 2021-03-12

Available Online: 2021-08-14

Abstract

Abstract

The Neumann boundary value problem about a class of Kirchhoff type equations with sign-changing potential terms was studied. By means of the variational method and the decomposition process for the underlying space, the energy functional was proved to satisfy the mountain pass geometry. Then, the energy functional (PS) sequence was proved to have a strongly convergent subsequence. Finally, the existence of two nontrivial solutions was obtained by Ekeland’s variational principle and the mountain pass lemma.
- Kirchhoff type equation,
- Neumann boundary value,
- mountain pass lemma,
- sign-changing potential

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References(15)

References

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