Heisenberg群上拟线性次椭圆方程无穷多解的存在性  

Existence of Infinitely Many Solutions to the Quasilinear Subelliptic Equations on Heisenberg Group

作　　者：何春雄[1] 陈树敏[1] 姚仰新[1] 

机构地区：[1]华南理工大学数学科学学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2005年第10期103-107,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10171032)

摘　　要：研究了加权Sobolev空间上拟线性次椭圆偏微分方程解的存在性,这里方程的非线性项是奇的.在较弱的条件下,证明方程所对应的泛函满足Cerami条件,进而应用Bartsch 的喷泉定理,得到了方程无穷多个大能量解的存在性.The existence for the solutions to the quasilinear subelliptic partial differential equations in a weighted Sobolev space is investigated in the condition that the nonlinear term is odd. Under comparably weaker conditions, the corresponding functional is proved to satisfy the Cerami condition. Moreover, by using the Fountain theorem of Bartsch, the existence of infinitely many solutions with large energy for the equations are obtained.

关 键 词：HEISENBERG群 拟线性 次椭圆方程 CERAMI条件 喷泉定理 加权SOBOLEV空间 

分 类 号：O175.25[理学—数学]