一类临界拟线性椭圆型方程非平凡解的存在性

摘要

A class of quasilinear elliptic equation involving critical Sobolev exponent was studied,and their reduction forms arose from the mathematical model in fluid mechanics and plasma physics.Under some suitable assumptions on the potential function,the existence of their nontrivial solutions is proved through using the constrained minimizing methods and concentration-compactness at infinity.%研究了一类带有临界Sobolev指数的拟线性椭圆型方程,该类方程的退化形式来源于流体力学、等离子物理中提出的数学模型.采用约束极小化方法和无穷远的集中紧性原理,在对位势函数作一些合适的假设下,证明了其非平凡解的存在性.