Heisenberg群上一类具变号权函数的拟线性次椭圆型方程的Nehari流形方法

摘要

本文研究了Heisenberg群上带有Dirichlet边界条件的拟线性次椭圆方程-?H,pu=λf(ξ)|u|p?2u+g(ξ)|u|r?2u.利用Nehari流形和纤维映射方法,获得了方程解的存在性以及多解性结果,同时说明了上述方程解的存在性是如何随着Nehari流形的性质而相应地改变,推广了欧氏空间中相应的结果.%In this paper, we investigate the Dirichlet problem for the following quasilinear sub-elliptic equation on the Heisenberg group ??H,pu = λf(ξ)|u|p?2u+g(ξ)|u|r?2u. Using the Nehari manifold and fibrering maps, we obtain the existence and multiplicity results of positive weak solution of the equation and show how existence results for positive solutions of the equation are linked to properties of the Nehari manifold, which generalize the corresponding results in Euclidean space.