Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904424 | Acta Mathematica Scientia | 2018 | 8 Pages |
Abstract
In this article, we study the nonexistence of solution with finite Morse index for the following Choquard type equation
-Îu=â«RN|u(y)|p|x-y|αdy|u(x)|p-2u(x)inRN,where N ⥠3, 0 < α < {4,N}. Suppose that 2 < p <
2N-αN-2, we will show that this problem does not possess nontrivial solution with finite Morse index. While for
p=2N-αN-2, if i(u) < â then we have
â«RNâ«RN|u(x)|p|u(y)|p|x-y|αdxdy<â and
â«RN|âu|2dx=â«RNâ«RN|u(x)|p|u(y)|p|x-y|αdxdy.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Xiaojun ZHAO,