| 摘要: |
| 本文中, 我们研究带有临界Sobolev指数的分数阶 p-q 拉普拉斯方程的非平凡解的存在性和多重性. 我们通过使用山路定理建立了问题非平凡弱解的存在性. 此外, 借助 Lusternik-Schnirelman 畴数理论, 我们还获得了解的多重性结果. |
| 关键词: 分数阶拉普拉斯, 山路定理, Lusternik-Schnirelman畴数理论 |
| DOI： |
| 分类号:O175.2 |
| 基金项目: |
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| Existence and multiplicity results for p-q Laplacian equation with critical Sobolev exponent |
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Fei Jiaying, 刘晓春
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Wuhan University
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| Abstract: |
| In this article, we deal with the existence and multiplicity of nontrivial solutions of the fractional p-q Laplacian equations involving the critical Sobolev exponent. We establish the existence theorem by Mountain Pass Theorem. Furthermore, we obtain the multiplicity results with the help of Lusternik-Schnirelman category theory. |
| Key words: Fractional p-q Laplacian, Mountain Pass Theorem, Lusternik-Schnirelman category theory |
