带竞争系数的拟线性方程基态解的存在性  

Existence of ground state solution for quasilinear equation with competing coefficients

作　　者：曾宇娇 胡亭曦 ZENG Yujiao;HU Tingxi(School of Mathematics Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《纺织高校基础科学学报》2023年第1期80-85,共6页Basic Sciences Journal of Textile Universities

基　　金：重庆师范大学博士启动基金(20XLB017);重庆市教委科学技术研究项目(KJQN202200515)。

摘　　要：考察一类含Sobolev次临界指标的拟线性椭圆型偏微分方程在无界区域上基态解的存在性,该方程含有2个在无穷远处趋向于常数的光滑位势函数。根据Ekland变分原理,问题被转化为求解方程对应的能量泛函在Nehari流形上约束极小的存在性;应用集中紧性原理,在一定的能量门槛条件下,约束变分问题的极小化序列被证明是相对紧的。给出了一个保证基态解存在的位势函数竞争性条件。It is investigated that the existence of ground state solution for a class of quasilinear elliptic PDEs involving the Sobolev subcritical nonlinearity. The impact of the competition between two potential functions is considered. By the Ekland′s variational principle, the ground states are obtained as the minimizers of the corresponding energy functional on the Nehari manifold. Using a concentration compactness argument, the minimization sequence of the constrained variational problem is proved to be relatively compact under a certain energy level. Finally, some geometric conditions are given to guarantee the existence of ground states.

关 键 词：拟线性方程 竞争系数 正基态解 Ekland变分原理 集中紧性原理 

分 类 号：O175.29[理学—数学]