| 一类具有变号位势Kirchhoff型方程解的存在性 |
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| 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. |
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| 作者姓名： | 雷俊 索洪敏 彭林艳 吴德科 蒙璐 |
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| 作者单位： | 贵州民族大学 数据科学与信息工程学院, 贵阳 550025 |
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| 基金项目： | 国家自然科学基金(11661021；11861021) |
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| 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.
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| 关 键 词： | Kirchhoff 型方程 Neumann边值 山路引理 变号位势 |
| 收稿时间： | 2020-09-17 |
Existence of Solutions for a Class of Kirchhoff Type Equations With Sign Changing Potential |
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| Affiliation: | School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, P.R.China |
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| 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. |
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