摘要
研究了Heisenberg群上一类含有临界Sobolev指数的偏微分方程解的存在性问题.利用Nehari流形以及极值原理,证明了在不同的条件下,方程至少存在一个或两个正解.
In this paper, we study the partial differential equations on the Heisenberg group with a singular potential and critical Sobolev exponent. With the help of Nehari manifold, we prove that our problem has at least one or two positive solutions under different conditions. The result generalized the corresponding result in Euclidean space.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2017年第3期478-490,共13页
Acta Mathematica Scientia
基金
国家自然科学基金(11171261
11371282)~~
