奇异椭圆方程对称解的存在性

Existence of symmetric solutions of a singular elliptic equation

研究了一类带奇性的p-Laplace方程,利用集中紧性原理,分s=0,s≠0两种情形对方程中可能存在的Dirac函数进行讨论,得到PS条件成立的最小能量水平,并通过一系列精巧的估计验证这个PS条件,得到方程G-对称解的存在性.

A class of singular p - Laplace equations is considered. Using the concentration-compact principle, the Dirac functions existed in this problem are discussed for the case of＂s = 0＂ and＂s 50＂ respectively. Then a minimal energy level is determined. This minimal energy level is the level which makes PS conditions of the problem hold. Finally through a series of exquisite estimates, the existence of G - symmetric solutions is obtained.