| 崔会敏,魏公明.带有变号势函数和Hardy项的临界p-双调和方程弱解的存在性[J].上海理工大学学报,2022,44(6):583-587. |
| 带有变号势函数和Hardy项的临界p-双调和方程弱解的存在性 |
| The existence of weak solutions for critical p-biharmonic equations with sign-changing weight function and Hardy term |
| 投稿时间：2021-10-23 |
| DOI：10.13255/j.cnki.jusst.20211023001 |
| 中文关键词: 山路引理 集中紧性原理 弱解 Hardy不等式 |
| 英文关键词:mountain pass lemma concentrative-compactness principle weak solution Hardy’s inequality |
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| 中文摘要: |
| 利用山路引理、集中紧性原理和Hardy不等式，研究了带有变号势函数和Hardy项的临界p-双调和方程弱解的存在性问题。首先验证了山路引理的几何条件，然后证明当$0 < \mu < {\mu _0}$，山路水平$c < \dfrac{2}{N} S^{N / 2 p}-\mu^{{p^*} /\left(p^*-q\right)}G$时满足${(PS)_c}$条件，最终证明了该类临界p-双调和方程至少存在一个非平凡弱解。 |
| 英文摘要: |
| The existence of weak solutions for critical p-biharmonic equations with sign-changing weight function and Hardy term was studied by using mountain pass lemma, concentration-compactness principle and Hardy’s inequality. Firstly, the geometric conditions of mountain pass lemma are verified. Next, if $0 < \mu < {\mu _0}$, ${(PS)_c}$ condition is satisfied when mountain level $c < \dfrac{2}{N} S^{N / 2 p}-\mu^{{p^*} /\left(p^*-q\right)}G$. Thus, it is proved that there exists at least one nontrivial weak solution for the given critical ${{p - }}$biharmonic equations. |
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