Journal of Shanghai University(Natural Science Edition) ›› 2015, Vol. 21 ›› Issue (03): 319-330.doi: 10.3969/j.issn.1007-2861.2013.07.052
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Abstract: Referring to the method of vector fields, this paper studies a class of semilinear quations on the Heisenberg group and gives a Liouville type theorem, namely, the nonexistence of nontrivial positive solutions. A class of real functional constituted by leftinvariant vector fields on the Heisenberg group is introduced. Some identities are obtained by identical deformation. It is proved that any nonnegative solution is trivial according to the properties of test function and some techniques such as polar coordinates formula on the Heisenberg group and Young inequality.
Key words: Heisenberg group, Liouville type theorem, semi-linear equation, vector field method
CLC Number:
O 175.2
ZHANG Shu-Tao, ZHAO Qiong, HAN Ya-Zhou. A Liouville type theorem of semi-linear equations on the Heisenberg group[J]. Journal of Shanghai University(Natural Science Edition), 2015, 21(03): 319-330.
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URL: https://www.journal.shu.edu.cn/EN/10.3969/j.issn.1007-2861.2013.07.052
https://www.journal.shu.edu.cn/EN/Y2015/V21/I03/319