具有临界指标的分数阶Kirchhoff型问题无穷多解的存在性

Existence of infinite many solutions for fractional Kirchhoff type equations with critical indexes

研究了一类带有临界指标和分数阶p-Laplace算子的Kirchhoff型问题,这类问题的解在实际问题中有着重要的应用。利用分数阶形式的集中紧致原理证明了紧性条件的成立,通过截断的技巧和新的对称山路引理获得了无穷多解的存在性,并且这些解收敛到零,改进了以前结果。

Consider a class of critical Kirchhoff type equations involving the fractional p-Laplacian operator.The solution of this kind of problems has important application in practical problems.The compactness condition is first proved by using the fractional version of concentration compactness principle,and then the existence of infinite many solutions is proved through the truncation technique and the Kajikiya’s new version of the symmetric mountain pass lemma.It shows that these solutions converge to zero,which fills the gap in the previous results.